Research Inventy : International Journal of Engineering and Science is published by the group of young academic and industrial researchers with 12 Issues per year. It is an online as well as print version open access journal that provides rapid publication (monthly) of articles in all areas of the subject such as: civil, mechanical, chemical, electronic and computer engineering as well as production and information technology. The Journal welcomes the submission of manuscripts that meet the general criteria of significance and scientific excellence. Papers will be published by rapid process within 20 days after acceptance and peer review process takes only 7 days. All articles published in Research Inventy will be peer-reviewed.
8 fixed point theorem in complete fuzzy metric space 8 megha shrivastavaBIOLOGICAL FORUM
ABSTRACT: In this paper our works establish a new fixed point theorem for a different type of mapping in complete fuzzy metric space. Here we define a mapping by using some proved results and obtain a result on the actuality of fixed points. We inspired by the concept of Hossein Piri and Poom Kumam [15]. They introduced the fixed point theorem for generalized F-suzuki -contraction mappings in complete b-metric space. Next Robert plebaniak [16] express his idea by result “New generalized fuzzy metric space and fixed point theorem in fuzzy metric space”. This paper also induces comparing of the outcome with existing result in the literature.
Keywords: Fuzzy set, Fuzzy metric space, Cauchy sequence Non- decreasing sequence, Fixed point, Mapping.
Semicompatibility and fixed point theorem in fuzzy metric space using implici...eSAT Publishing House
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
8 fixed point theorem in complete fuzzy metric space 8 megha shrivastavaBIOLOGICAL FORUM
ABSTRACT: In this paper our works establish a new fixed point theorem for a different type of mapping in complete fuzzy metric space. Here we define a mapping by using some proved results and obtain a result on the actuality of fixed points. We inspired by the concept of Hossein Piri and Poom Kumam [15]. They introduced the fixed point theorem for generalized F-suzuki -contraction mappings in complete b-metric space. Next Robert plebaniak [16] express his idea by result “New generalized fuzzy metric space and fixed point theorem in fuzzy metric space”. This paper also induces comparing of the outcome with existing result in the literature.
Keywords: Fuzzy set, Fuzzy metric space, Cauchy sequence Non- decreasing sequence, Fixed point, Mapping.
Semicompatibility and fixed point theorem in fuzzy metric space using implici...eSAT Publishing House
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
International Journal of Mathematics and Statistics Invention (IJMSI) inventionjournals
International Journal of Mathematics and Statistics Invention (IJMSI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJMSI publishes research articles and reviews within the whole field Mathematics and Statistics, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
Common Fixed Point Theorems For Occasionally Weakely Compatible Mappingsiosrjce
Som [11 ] establishes a common fixed point theorem for R-weakly Commuting mappings in a Fuzzy
metric space.The object of this Paper is to prove some fixed point theorems for occasionally Weakly compatible
mappings by improving the condition of Som[11 ].
Fixed Point Results In Fuzzy Menger Space With Common Property (E.A.)IJERA Editor
This paper presents some common fixed point theorems for weakly compatible mappings via an implicit relation in Fuzzy Menger spaces satisfying the common property (E.A)
Research Inventy : International Journal of Engineering and Science is published by the group of young academic and industrial researchers with 12 Issues per year. It is an online as well as print version open access journal that provides rapid publication (monthly) of articles in all areas of the subject such as: civil, mechanical, chemical, electronic and computer engineering as well as production and information technology. The Journal welcomes the submission of manuscripts that meet the general criteria of significance and scientific excellence. Papers will be published by rapid process within 20 days after acceptance and peer review process takes only 7 days. All articles published in Research Inventy will be peer-reviewed.
Some new exact Solutions for the nonlinear schrödinger equationinventy
Research Inventy : International Journal of Engineering and Science is published by the group of young academic and industrial researchers with 12 Issues per year. It is an online as well as print version open access journal that provides rapid publication (monthly) of articles in all areas of the subject such as: civil, mechanical, chemical, electronic and computer engineering as well as production and information technology. The Journal welcomes the submission of manuscripts that meet the general criteria of significance and scientific excellence. Papers will be published by rapid process within 20 days after acceptance and peer review process takes only 7 days. All articles published in Research Inventy will be peer-reviewed.
Research Inventy : International Journal of Engineering and Scienceinventy
Research Inventy : International Journal of Engineering and Science is published by the group of young academic and industrial researchers with 12 Issues per year. It is an online as well as print version open access journal that provides rapid publication (monthly) of articles in all areas of the subject such as: civil, mechanical, chemical, electronic and computer engineering as well as production and information technology. The Journal welcomes the submission of manuscripts that meet the general criteria of significance and scientific excellence. Papers will be published by rapid process within 20 days after acceptance and peer review process takes only 7 days. All articles published in Research Inventy will be peer-reviewed.
Research Inventy : International Journal of Engineering and Scienceinventy
esearch Inventy : International Journal of Engineering and Science is published by the group of young academic and industrial researchers with 12 Issues per year. It is an online as well as print version open access journal that provides rapid publication (monthly) of articles in all areas of the subject such as: civil, mechanical, chemical, electronic and computer engineering as well as production and information technology. The Journal welcomes the submission of manuscripts that meet the general criteria of significance and scientific excellence. Papers will be published by rapid process within 20 days after acceptance and peer review process takes only 7 days. All articles published in Research Inventy will be peer-reviewed.
Research Inventy : International Journal of Engineering and Science is published by the group of young academic and industrial researchers with 12 Issues per year. It is an online as well as print version open access journal that provides rapid publication (monthly) of articles in all areas of the subject such as: civil, mechanical, chemical, electronic and computer engineering as well as production and information technology. The Journal welcomes the submission of manuscripts that meet the general criteria of significance and scientific excellence. Papers will be published by rapid process within 20 days after acceptance and peer review process takes only 7 days. All articles published in Research Inventy will be peer-reviewed.
International Journal of Mathematics and Statistics Invention (IJMSI) inventionjournals
International Journal of Mathematics and Statistics Invention (IJMSI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJMSI publishes research articles and reviews within the whole field Mathematics and Statistics, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
Common Fixed Point Theorems For Occasionally Weakely Compatible Mappingsiosrjce
Som [11 ] establishes a common fixed point theorem for R-weakly Commuting mappings in a Fuzzy
metric space.The object of this Paper is to prove some fixed point theorems for occasionally Weakly compatible
mappings by improving the condition of Som[11 ].
Fixed Point Results In Fuzzy Menger Space With Common Property (E.A.)IJERA Editor
This paper presents some common fixed point theorems for weakly compatible mappings via an implicit relation in Fuzzy Menger spaces satisfying the common property (E.A)
Research Inventy : International Journal of Engineering and Science is published by the group of young academic and industrial researchers with 12 Issues per year. It is an online as well as print version open access journal that provides rapid publication (monthly) of articles in all areas of the subject such as: civil, mechanical, chemical, electronic and computer engineering as well as production and information technology. The Journal welcomes the submission of manuscripts that meet the general criteria of significance and scientific excellence. Papers will be published by rapid process within 20 days after acceptance and peer review process takes only 7 days. All articles published in Research Inventy will be peer-reviewed.
Some new exact Solutions for the nonlinear schrödinger equationinventy
Research Inventy : International Journal of Engineering and Science is published by the group of young academic and industrial researchers with 12 Issues per year. It is an online as well as print version open access journal that provides rapid publication (monthly) of articles in all areas of the subject such as: civil, mechanical, chemical, electronic and computer engineering as well as production and information technology. The Journal welcomes the submission of manuscripts that meet the general criteria of significance and scientific excellence. Papers will be published by rapid process within 20 days after acceptance and peer review process takes only 7 days. All articles published in Research Inventy will be peer-reviewed.
Research Inventy : International Journal of Engineering and Scienceinventy
Research Inventy : International Journal of Engineering and Science is published by the group of young academic and industrial researchers with 12 Issues per year. It is an online as well as print version open access journal that provides rapid publication (monthly) of articles in all areas of the subject such as: civil, mechanical, chemical, electronic and computer engineering as well as production and information technology. The Journal welcomes the submission of manuscripts that meet the general criteria of significance and scientific excellence. Papers will be published by rapid process within 20 days after acceptance and peer review process takes only 7 days. All articles published in Research Inventy will be peer-reviewed.
Research Inventy : International Journal of Engineering and Scienceinventy
esearch Inventy : International Journal of Engineering and Science is published by the group of young academic and industrial researchers with 12 Issues per year. It is an online as well as print version open access journal that provides rapid publication (monthly) of articles in all areas of the subject such as: civil, mechanical, chemical, electronic and computer engineering as well as production and information technology. The Journal welcomes the submission of manuscripts that meet the general criteria of significance and scientific excellence. Papers will be published by rapid process within 20 days after acceptance and peer review process takes only 7 days. All articles published in Research Inventy will be peer-reviewed.
Research Inventy : International Journal of Engineering and Science is published by the group of young academic and industrial researchers with 12 Issues per year. It is an online as well as print version open access journal that provides rapid publication (monthly) of articles in all areas of the subject such as: civil, mechanical, chemical, electronic and computer engineering as well as production and information technology. The Journal welcomes the submission of manuscripts that meet the general criteria of significance and scientific excellence. Papers will be published by rapid process within 20 days after acceptance and peer review process takes only 7 days. All articles published in Research Inventy will be peer-reviewed.
Research Inventy : International Journal of Engineering and Science is published by the group of young academic and industrial researchers with 12 Issues per year. It is an online as well as print version open access journal that provides rapid publication (monthly) of articles in all areas of the subject such as: civil, mechanical, chemical, electronic and computer engineering as well as production and information technology. The Journal welcomes the submission of manuscripts that meet the general criteria of significance and scientific excellence. Papers will be published by rapid process within 20 days after acceptance and peer review process takes only 7 days. All articles published in Research Inventy will be peer-reviewed.
Research Inventy : International Journal of Engineering and Science is published by the group of young academic and industrial researchers with 12 Issues per year. It is an online as well as print version open access journal that provides rapid publication (monthly) of articles in all areas of the subject such as: civil, mechanical, chemical, electronic and computer engineering as well as production and information technology. The Journal welcomes the submission of manuscripts that meet the general criteria of significance and scientific excellence. Papers will be published by rapid process within 20 days after acceptance and peer review process takes only 7 days. All articles published in Research Inventy will be peer-reviewed.
Semicompatibility and fixed point theorem in fuzzy metric space using implici...eSAT Journals
Abstract In this paper we proved fixed point theorem of four mapping on fuzzy metric space based on the concept of semi copatibility using implicit relation. These results generalize several corresponding relations in fuzzy metric space. All the results of this paper are new. Keywords: fuzzy metric space, compatibility, semi compatibility, implicit relation. 2000 AMS Mathematics Subject Classification: 47H10, 54H25
Common Fixed Point Theorems in Compatible Mappings of Type (P*) of Generalize...mathsjournal
In this paper, we give some new definition of Compatible mappings of type (P), type (P-1) and type (P-2) in intuitionistic generalized fuzzy metric spaces and prove Common fixed point theorems for six mappings
under the conditions of compatible mappings of type (P-1) and type (P-2) in complete intuitionistic fuzzy
metric spaces. Our results intuitionistically fuzzify the result of Muthuraj and Pandiselvi [15]
Mathematics subject classifications: 45H10, 54H25
IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
Fixed points of contractive and Geraghty contraction mappings under the influ...IJERA Editor
In this paper, we prove the existence of fixed points of contractive and Geraghty contraction maps in complete metric spaces under the influence of altering distances. Our results extend and generalize some of the known results.
COMMON FIXED POINT THEOREMS IN COMPATIBLE MAPPINGS OF TYPE (P*) OF GENERALIZE...mathsjournal
In this paper, we give some new definition of Compatible mappings of type (P), type (P-1) and type (P-2) in intuitionistic generalized fuzzy metric spaces and prove Common fixed point theorems for six mappings under the conditions of compatible mappings of type (P-1) and type (P-2) in complete intuitionistic fuzzy metric spaces. Our results intuitionistically fuzzify the result of Muthuraj and Pandiselvi [15]
COMMON FIXED POINT THEOREMS IN COMPATIBLE MAPPINGS OF TYPE (P*) OF GENERALIZE...mathsjournal
In this paper, we give some new definition of Compatible mappings of type (P), type (P-1) and type (P-2) in intuitionistic generalized fuzzy metric spaces and prove Common fixed point theorems for six mappings under the conditions of compatible mappings of type (P-1) and type (P-2) in complete intuitionistic fuzzy metric spaces.
COMMON FIXED POINT THEOREMS IN COMPATIBLE MAPPINGS OF TYPE (P*) OF GENERALIZE...mathsjournal
In this paper, we give some new definition of Compatible mappings of type (P), type (P-1) and type (P-2) in intuitionistic generalized fuzzy metric spaces and prove Common fixed point theorems for six mappings under the
conditions of compatible mappings of type (P-1) and type (P-2) in complete intuitionistic fuzzy metric spaces. Our results intuitionistically fuzzify the result of Muthuraj and Pandiselvi [15]
Mathematics subject classifications: 45H10, 54H25
Fixed Point Theorem in Fuzzy Metric Space Using (CLRg) Propertyinventionjournals
The object of this paper is to establish a common fixed point theorem for semi-compatible pair of self maps by using CLRg Property in fuzzy metric space.
Fixed Point Theorem in Fuzzy Metric SpaceIJERA Editor
In this present paper on fixed point theorems in fuzzy metric space . we extended to Fuzzy Metric space
generalisation of main theorem .
Mathematics Subject Classification: 47H10, 54A40
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
Experimental Investigation of a Household Refrigerator Using Evaporative-Cool...inventy
The objective of this paper was to investigate experimentally the effect of Evaporative-cooled condenser in a household refrigerator. The experiment was done using HCF134a as the refrigerant. The performance of the household refrigerator with air-cooled and Evaporative-cooled condenser was compared for different load conditions. The results indicate that the refrigerator performance had improved when evaporative-cooled condenser was used instead of air-cooled condenser on all load conditions. Evaporativecooled condenser reduced the energy consumption when compared with the air-cooled condenser. There was also an enhancement in coefficient of performance (COP) when evaporative-cooled condenser was used instead of air-cooled condenser. The Evaporative cooled heat exchanger was designed and the system was modified by retrofitting it, instead of the conventional air-cooled condenser by making drop wise condensation using water and forced circulation over the condenser. From the experimental analysis it is observed that the COP of evaporative cooled system increased by 13.44% compared to that of air cooled system. So the overall efficiency and refrigerating effect is increased. In minimum constructional, maintenance and running cost, the system is much useful for domestic purpose. This study also revealed that combining a evaporative cooled system along with conventional water cooled system under the condition that the defrost water obtained from the freezer is used for drop wise condensation over condenser and water cooled condensation of the condenser at the bottom using remaining defrost water would reduce the power consumption, work done and hence further increase in refrigerating effect of the system. The study has shown that such a system is technically feasible and economically viable
Copper Strip Corrossion Test in Various Aviation Fuelsinventy
This research work takes in to account of corrosiveness test on various aviation fuels in the state of Telengana (India). The purpose of this experiment is to determine the corrosiveness test of fuels. This determination will be accomplished by using copper strip corrosion test by using the copper strip experiment we can determine the corrosive property of the fuel and hence the efficiency of fuel. The research covers the importance of knowing the corrosive property of different petroleum fuels including aviation turbine fuel.
Additional Conservation Laws for Two-Velocity Hydrodynamics Equations with th...inventy
A series of the differential identities connecting velocities, pressure and body force in the twovelocity hydrodynamics equations with equilibrium of pressure phases in reversible hydrodynamic approximation is obtaned.
Comparative Study of the Quality of Life, Quality of Work Life and Organisati...inventy
People’s lives are increasingly centred on work; they spend at least one-third of their time within the organisations that employ them. Investigating the factors that interfere with employees’ well-being and the organisational environment is becoming an increasing concern in organisations. This article identifies the criteria of the quality of life (QoL), quality of working life (QWL) and organisational climate instruments to point out their similarities. For bibliographic construction and data research, articles were sought in national and international journals, books and dissertations/articles in SciELO, Science Direct, Medline and Pub Med databases. The results show direct relationships amongst QoL, QWL and organisational climate instruments. The relationship between QoL and QWL instruments is based on fair compensation, social interaction, organisational communication, working conditions and functional capacity. QWL and organisational climate instruments are related through social interaction and interfaces. QoL and organisational climate instruments are related based on social interaction, organisational communication, and work conditions.
A Study of Automated Decision Making Systemsinventy
The decision making process of many operations are dependent on analysing very large data sets, previous decisions and their results. The information generated from the large data sets are used as an input for making decisions. Since the decisions to be taken in day to day operations are expanding, the time taken for manual decision making is also expanding. In order to reduce the time, cost and to increase the efficiency and accuracy, which are the most important things for customer satisfaction, many organisations are adopting the automated decision making systems. This paper is about the technologies used for automated decision making systems and the areas in which automated decisions systems works more efficiently and accurately.
Crystallization of L-Glutamic Acid: Mechanism of Heterogeneous β -Form Nuclea...inventy
The mechanism of heterogeneous nucleation of β-form L-glutamic acid was deeply investigated in cooling crystallization. The present study found that the β-form crystals were epitaxially grown on the α-form crystals and they were preferably crystallized on the (011) and (001) surfaces instead of the (111) surfaces of α- form crystals. This result was explained via the molecular simulation. The molecular simulation indicated that the different surfaces of α-form crystals provided different functional groups, resulting in different sites for the heterogeneous nucleation of β-form crystals. Here, the functional group were COO- , C=O and O-H on the (011) and (001) surfaces of α-form crystals, respectively, while it was the NH3 + on the (111) surfaces of α-form crystals. As such, the degree of lattice matching (E) between the β-form crystals and the various surfaces of α- form crystal was distinguished, where the degree of lattice matching (E) between the β-form crystals and the (011), (001) and (111) surfaces of α-form crystal were estimated as 5.30, 5.25 and 2.39, respectively, implying that the (011) and (001) surfaces of α-form crystal were more favorable to generate the heterogeneous nucleation of β-form crystals than the (111) surfaces of α-form crystal
Evaluation of Damage by the Reliability of the Traction Test on Polymer Test ...inventy
In recent decades, polymers have undergone a remarkable historical development and their use has been greatly imposed by gradually dethroning most of the secular materials. These polymer materials have always distinguished themselves by their simple shaping and inexpensive price, their versatility, lightness, and chemical stability but despite their massive use in everyday life as well as in advanced technologies. Generally, these materials still not understood which requires a thorough knowledge of their chemical, physical, rheological and mechanical properties. This paper, we study the mechanical behavior of an amorphous polymer: Acrylonitrile Butadiene Styrene “ABS” by means of uniaxial tensile testing on pierced test pieces with different notch lengths ranging between 1 to 14mm.The proposed approach consists in analyzing the evolution of the global geometry of the obtained strain curves by taking into account the zones and characteristic points of these curves as well as the effect of the damage on the mechanical behavior of the polymer ABS, in order to visualize the evolution of the damage by a static model
Application of Kennelly’model of Running Performances to Elite Endurance Runn...inventy
: The model of Kennelly between distance (Dlim) and exhaustion time (tlim) has been applied to the individual performances of 19 elite endurance runners (World-record holders and Olympic winners) from P. Nurmi (1920-1924) to M. Farah (2012) whose individual best performances on several different distances are known. Kennelly’s model (Dlim = k tlim ) can describe the individual performances of elite runners with a high accuracy (errors lower than 2 %). There is a linear relationship between parameters k and exponents of the elite runners and the extreme values correspond to S. Coe (k = 15.8; = 0.851) and E. Zatopek (k = 6.57; = 0.984). Exponent can be considered as a dimensionless index of aerobic endurance which is close to 1 in the best endurance runners. If it is assumed than maximal aerobic speed can be maintained 7 min in elite endurance runners, exponent is equal to the normalized critical speed (critical speed/maximal aerobic speed) computed from exhaustion times equal to 3 and 12.5 min in these runners.
Development and Application of a Failure Monitoring System by Using the Vibra...inventy
In this project, a failure monitoring system is developed by using the vibration and location information of balises in railway signaling. A lot of field equipment in railway are loosening and broken in time period so that they need maintenance due to the vibrations that occur due to high speed trains traffic and railway vehicles impact. Among the field equipment, balises have very important role of communication in terms of transmitting information to trains. In this scope, it is aimed to make maintenance works more efficient, have no delayed trains, detect previously failure location and intervene in failure timely, by detecting and controlling balise cases such as loosening, out of place and the data consistency error that happens because of balise physical state. In this project, the communication is provided with I2C, Modbus RTU (Remote Terminal Unit) and RS485 standards by using Arduino Uno cards and MPU6050 IMU (Inertial Measurement Unit) sensors in laboratory. Each used sensors are in slave mode and computer interface designed with C# is in master mode. Fault situations in the system are checked instant by the interface. (it is assumed to mount the IMU sensor and the Arduino circuit on the balise) it is seen that the interface responds to the sensor movements instant and the system works well in the end of test processes.
The Management of Protected Areas in Serengeti Ecosystem: A Case Study of Iko...inventy
The study assessed the management of protected areas in Serengeti ecosystem using the case of IGGRs. Specifically, the study aimed at identifying the strategies used for natural resources management; examining the impacts of those strategies; examining the hindrances of the identified strategies; and lastly, examining the methods for scaling up the performance of strategies used for natural resources in the study area. The study involved two villages among 31 villages bordering IGGRs where in each village; at least 5% of the households were sampled. Both Primary data and secondary data were collected and analyzed both manually and computer by using SPSS software. The study revealed that, study population ranked IGGRs performance on protection of natural resources, especially on conserving wildlife for future generation and in reducing poaching to be good(53.3%). In addition, the relationship with IGGRs was said to be considerable good (46.7%). In the aspect of reducing poaching, the findings show that poaching has been reduced by 96.2% from 2009 to 2012. Furthermore, 81.4% of respondents said they use different strategies to control loss of natural resources which in turn has considerably improved the relationship between protected areas and the surrounding communities in some of the aspects. Despite of above successes, the study findings has revealed a number of challenges that hinders the full attainment of conservation objectives. Among the challenges are loss of life and properties (86.4%), shortage of water for livestock (68.9%) since water sources such as Grumeti and Rubana rivers are within protected area while the adjacent local communities do not have a free access to those water sources. Other challenges especially on the IGGRs management include insufficient fund base, working facilities and inadequate staffs. Based on the above findings, the study concluded that the strategies used for natural resources management of protected areas in Serengeti ecosystem is fairly sustainable and need functional participatory approaches of local people and other stakeholders in order to bring about a collaborative natural resources management network in the ecosystem. Furthermore, based on the findings above, equity in benefit sharing accrued from natural resource management in protected areas, more financial support to IGGRs and local community, the use of non-lethal deterrents for crop protection, integration of croplivestock production systems, adoption of land use plans as a solution to land conflicts, strengthens of community based conservation (CBC), adoption of modern information technology such as geographical information system (GIS) and remote sensing are recommended.
Size distribution and biometric relationships of little tunny Euthynnus allet...inventy
This study is taken from data of commercial fishing of the little tunny, Euthynnus alletteratus (Rafinesque, 1810) caught in the Algerian coast, sampled between november 2011 and april 2016. Data were collected in order to determine size distributions of the population and biometric relationships of species including the size - weight relationships. A total of 601 fish ranged from 30.9 and 103 cm fork length (FL) were observed. The size distribution of Euthynnus alletteratus shows multiple modal values witch the most important cohort corresponds to the age class 2 (42-46 cm). The value of the allometric coefficient (b) of the FL/TW relationship is lower than 3, indicating a negative allometric growth.
Removal of Chromium (VI) From Aqueous Solutions Using Discarded Solanum Tuber...inventy
Industrial polluting effluents containing heavy metals are of serious environmental concern in India. Chromium is frequently used in industries like electroplating, metal finishing, cooling towers, dyes, paints, anodizing and leather tanning and is found as traces in effluents finding their way to natural water bodies causing hazardous toxicity to the health of humans, animals and aquatic lives directly or indirectly. Many methods for the removal of Chromium such as chemical reduction, precipitation, ion exchange, electrochemical reduction, evaporation, reverse osmosis and adsorption using activated carbon etc. have been reported but all being expensive and complicated to operate. Experimental practices reveal that adsorption by agricultural and horticultural wastes are quite simple, inexpensive and efficient method. Agra is famous for Potato farming, a lot of discarded potato waste from cold storages is thrown along road side drains causing solid waste generated which either creates solid waste disposal problem or otherwise it finds way to Yamuna river resulting high BOD and posing a serious threat to the aquatic environment. For developing countries like India adsorption studies using discarded potato (Solanum tuberosum) waste from cold storages (DPWC) a solid waste as low cost adsorbent for Chromium removal was dual beneficial i.e., an ideal solution to these solid wastes disposal problem of Agra and removal of Chromium from tannery effluents and thereby saving aquatic life from Chromium contamination in Yamuna river. Keeping this in view batch experiments were designed to study the feasibility of discarded potato waste from cold storages to remove chromium (VI) from the aqueous solutions. During the study various affecting parameters, such as pH, adsorbent does, initial concentration, temperature, contact time, adsorbent grain size and start up agitation speed were optimized as 5.0, 10-20 g/l, 50 mg/l, 250C, 135 minutes, average size and 80 rpm respectively on chromium removal efficiency. Various Isotherms such as Langmuir, Freundlich, Tempkin also fitted suitably and various corresponding constants determined from these Isotherms favor and support the adsorption. Thermodynamic constants ∆G, ∆H and ∆S were found to be 0.267 KJ/mole, 0.288 KJ/mole and 0.0013 KJ/mole respectively.
Effect of Various External and Internal Factors on the Carrier Mobility in n-...inventy
The effect of various external (temperature, electric field, light) and intracrystalline (doping, initial resistivity) factors on the mobility of carriers in layered n-InSe semiconductor experimentally have been investigated. Scientific explanations of the results are proposed
Transient flow analysis for horizontal axial upper-wind turbineinventy
This study is to carry out a transient flow field analysis on the condition that the wind turbine is working to generate turbine, the wind turbine operating conditions change over time, Purpose of this study is try to find out the rule from the wind turbine changing over time . In transient analysis, the wind velocity on inlet boundary and rotation speed in the rotor field will change over time, and an analytical process is provided that can be used for future reference. At present, the wind turbine model is designed on the concept of upwind horizontal axis type. The computer engineering software GH Bladed is used to obtain the relationship between the rotor velocity and the wind turbine. Then the ANSYS engineering software is used to calculate the stress and strain distribution in the blades over time. From the analytical result, the relationship between the stress distribution in the blades and the rotor velocity is got to be used as a reference for future wind turbine structural optimization.
Choice of Numerical Integration Method for Wind Time History Analysis of Tall...inventy
Wind tunnel tests are being performed routinely around the world for designing tall buildings but the advent of powerful computational tools will make time-history analysis for wind more common in near future. As the duration of wind storms ranges from tens of minutes to hours while earthquake durations are typically less than a three to four minutes, the choice of a time step size (Δt) for wind studies needs to be much larger both to reduce the computational time and to save disk space. As the error in any numerical solution of the equation of motion is dependent on step size (Δt), careful investigations on the choice of numerical integration methods for wind analyses are necessary. From a wide variety of integration methods available, it was decided to investigate three methods that seem appropriate for 3D-time history analysis of tall buildings for wind. These are modal time history analysis, the Hilber-Hughes-Taylor (HHT) method or α-method with α=- 0.1, and the Newmark method with β=0.25 and γ=0.5 ( i.e., trapezoidal rule). SAP2000, a common structural analysis software tool, and a 64-story structure are used to conduct all the analyses in this paper. A boundary layer wind tunnel (BLWT) pressure time history measured at 120 locations around the building envelope of a similar structure is used for the analyses. Analyses performed with both the HHT and Newmark-method considering P-delta effects show that second order effects have a considerable impact on both displacement and acceleration response. This result shows that it is necessary to account P-delta effect for wind analysis of tall buildings. As the direct integration time history analysis required very large computation times and very large computer physical memory for a wind duration of hours, a modal analysis with reduced stiffness is considered as a good alternative. For that purpose, a non-linear static analysis of the structure with a load combination of 1.0D + 1.0L is performed in SAP2000 and the reduced stiffness of the structure after the analysis is used to conduct an eigenvalue analysis to extract the mode shapes and frequencies of this structure. Then the first 20- modes are used to perform a modal time history analysis for wind load. The result shows that the responses from modal analysis with “20-mode (reduced stiffness)” are comparable with that from the P-Δ analyses of Newmark-method
Impacts of Demand Side Management on System Reliability Evaluationinventy
Electricity demand in Saudi Arabia is steadily increasing as electrical loads grows at a rate of about 7% per year, this represents a high rate by all standards, and largely due to population growth, as well as due to government subsidies which may lead to prices much lower than actual production cost. This growth represents a challenge that requires Saudi Electricity Company (SEC) to invest huge amounts of money every year, for the construction of additional generation capacity along with the reinforcement of transmission network to meet the consumption growth.Also the demand varies frequently throughout the day, causing a waste of a large part of the energy. SEC believes the optimum solution lies in altering the load shape in order to have a better balance between customer’s consumption and SEC’s generation, This paper describes the method for improving the power system reliability by shifting the portion of peak load to off-peak periods This load management scheme can be achieved by lifting the generation during off peak periods and utilizing the stored energy during peak periods. A hybrid set up involving solar and wind energy along with batteries can also be used to store energy and utilize it during peak periods.
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The capacitors are increasingly being used as energy storage devicesin various power systems. The scientists of the world are tryingto maximize the electrical capacity of the supercapacitors. To achieve this purpose, numerous method sare used: the surface activation of electrodes, the surface etching using the electronbeam, the electrode etching with variousgasplasma, etc. The purpose of this work is toresearch how the properties of carbon electrodes depend on the plasma parameters at whichtheywere formed. The largest surface area ofcarbonelectrodeof47.25m2 /gis obtainedat 15 ofAr/C2H2gasratio. Meanwhile, theSEMimages show that the disruption of structures with low bond energies and the formation of new onesare taking place when the carbon electrodes are etched at acetylene plasma and placed on carbon electrode. The measurements of capacitance showthat capacitors with affectedelectrodes have about10-15% highercapacity than those not treated with acetyleneplasma.
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20240605 QFM017 Machine Intelligence Reading List May 2024
B043007014
1. Research Inventy: International Journal Of Engineering And Science
Vol.4, Issue 3(March 2014), PP 07-14
Issn (e): 2278-4721, Issn (p):2319-6483, www.researchinventy.com
7
New results on Occasionally Weakly Compatible Mappingsand
Fixed point Theorem in Fuzzy Metric Spaces Satisfying Integral
Type Inequality
1
S.k.Malhotra, 2
Vineeta Singh
1Department of Mathematics, Govt. S.G.S. P.G. College,Ganjbasoda (M.P.)
2Department of Mathematics, S.A.T.I. Dist. Vidisha (M.P.) INDIA
Abstract: The aim of this paper is to present some new common fixed point theorem in fuzzy metric spaces for
occasionally weakly compatible mappings with integral type inequality by reducing its minimum value.
Keywords: Fuzzy metric space, occasionally weakly compatible (owc) mappings, common fixed point.
I. INTRODUCTION:
Fuzzy set was defined by Zadeh [26]. Kramosil and Michalek [14] introduced fuzzy metric space, many authors
extend their views, Grorge and Veermani [6] modified the notion of fuzzy metric spaces with the help of continuous t-norms
Grabiec[7], Subramanyam[28],Vasuki[25], Pant and Jha,[20] obtained some analogous results proved by Balasubramaniam
et al. Subsequently, it was developed extensively by many authors and used in various fields, Jungck [10] introduced the
notion of compatible maps for a pair of self maps. Several papers have come up involving compatible mapping proving the
existence of common fixed points both in the classical and fuzzy metric spaces.
The theory of fixed point equations is one of the basic tools to handle various physical formulations. Fixed point
theorems in fuzzy mathematics has got a direction of vigorous hope and vital trust with the study of Kramosil and Michalek
[14], who introduced the concept of fuzzy metric space. Later on this concept of fuzzy metric space was modified by George
and Veermani [6] Sessa [27] initiated the tradition of improving commutative condition in fixed point theorems by
introducing the notion of weak commuting property. Further Juncgk [10] gave a more generalized condition defined as
compatibility in metric spaces.
Jungck and Rhoades [11] introduced the concept of weakly compatible maps which were found to be more
generalized than compatible maps. Grabiec [7] obtained fuzzy version of Banach contraction principle. Singh and M.S.
Chauhan [29] brought forward the concept of compatibility in fuzzy metric space. Pant [18, 19, 20] introduced the new
concept reciprocally continuous mappings and established some common fixed point theorems. Balasubramaniam et al. [4],
have shown that Rhoades [22] open problem on the existence of contractive definition which generates a fixed point but does
not force the mappings to be continuous at the fixed point, posses an affirmative answer. Recent literature in fixed point in
fuzzy metric space can be viewed in
[1, 2, 9, 16, 24]. This paper offers the fixed point theorems on fuzzy metric spaces which generalize extend and fuzzify
several known fixed point theorems for occasionally compatible maps on metric space by making use of
integral type inequality.
II. PRELIMINARY NOTES:
Definition 2.1 [26] A fuzzy set A in X is a function with domain X and values in [0,1].
Definition 2.2 [23] A binary operation: [0, 1] × [0,1]→ [0, 1] is a continuous t-norms if it satisfies the
following conditions:
(i) *is associative and commutative
(ii) *is continuous;
(iii) a*1 = a for all a [0,1];
a*b ≤ c*d whenever a ≤ c and b ≤ d, and a, b, c, d [0,1].
Definition 2.3. A triplet (X,M,∗ ) is said to be a fuzzy metric space if X is an arbitrary set,
∗ is a continuous t−norm and M is a fuzzy set on X 2
×(0,∞) satisfying the following;
(FM-1) M(x,y,t)>0
(FM-2) M(x,y,t)=1if and only if x=y.
(FM-3) M(x,y,t)=M(y,x,t)
(FM-4) M(x,y,t)∗ M(y,z,s)≤M(x,z,t +s)
(FM-5) M(x,y,•):(0,∞)→(0,1] is left continuous.
2. New results on Occasionally Weakly Compatible Mappingsand…
8
(X,M,*) denotes a fuzzy metric space ,(x,y,t) can be thought of as
degree of nearness between x and y with respect to
1. we identify x=y with M(x,y,t)=1
for all t >0
in following example every metric induces a fuzzy metric.
Example 2.4 Let X = [0,1], t-norm defined by a*b = min{a,b} where a,b [0,1] and M is the fuzzy set on
X2
× (0, ∞) defined by M(x,y,t) = ( exp(!x-y!)/t)-1
for all x,y X, t > 0. Then (X,M,*) is a fuzzy metric
space.
Example 2.5 (Induced fuzzy metric [6]) Let (X, d) be a metric space, denote a * b = a.b & for all a,b [0,1]
and let Md be fuzzy sets on X2
× (0, ∞) defined as follows
Md(x,y,t) = (t/(t+d(x,y)
Then (X,M,*) is a fuzzy metric space. We call this fuzzy metric induced by a metric d as the standard
intuitionistic fuzzy metric.
Definition 2.6 [11] Two self mappings f and g of a fuzzy metric space (X,M,*) are called compatible if
lim n→∞ M (fgxn,gfxn, t) = 1 wherever { xn} is sequence in X such that
lim n→∞ fxn = lim n→∞ gxn = x for some x in X
Definition 2.7 [5] Two self maps f and g of a fuzzy metric space (X, M,*) are called reciprocally
continuous on X if
lim n→∞ fxn = fx and
lim n→∞ gfxn = gx
wherever { xn} is sequence in X such that
lim n→∞fxn = lim n→∞gxn = x for some x in X.
Definition 2.8 [6] : Let (X,M,*) be a fuzzy metric space. Then
(a) A sequence {xn }in X is said to converges to x in X if for each > 0 and each t > 0, there exist no N
such that M ( xn , x ,t ) > 1 for all n .> no..
(b) A sequence {xn } in X is said to be Cauchy if for each > 0 and each t > 0, there exist no N such that M
( xn , xm ,t ) > 1 – for all n, m no..
(c) A fuzzy metric space in which every Cauchy sequence is convergent is said to be complete.
Definition 2.9 Two self maps f and g of a set X are occasionally weakly compatible (owc) iff there is a
point x in X which is a coincidence point of f and g at which f and g commute.
Al-Thagafi and Naseer Shahzad [3] shown that occasionally weakly is weakly compatible but converse
is not true.
Definition 2.10 Let (X,d) be a compatible metric space, [0,1], f:X→X a mapping such that for
each x,y X d(fx,fy)
∫0 dtt )( ≤
),(
0
)(
yxd
dtt
where R: T
→R
lebesgue integral mapping which is summable,
> 0,
0
)( dtt >0
3. New results on Occasionally Weakly Compatible Mappingsand…
9
nonnegative and such that, for each. Then f has a unique common fixed z X such that for each x X
lim n→∞ fn
x =z
Rhodes[30], extended this resul by replacing the above condition by the following
),(
0
)(fyfxd dtt
≤
)(,(),((2/1),,(),,(),,(max(
0
)(
xfxdfyxdfyydfxxdyxd
dtt
Ojha et al.(2010). Let (X,d) be a metric space and let f:X→X F:X→CB(X) be single and a multi valued map
respectively, suppose that t and are occasionally weakly commutative (owc) and satisfy the inequality
pFxFxd FxfydFyfxcdpFyfydpFxfxad
FyfydpFxfxdpfyfxad
dttdtt
),(
0
),(),(1),(1),(
),(1),,(1),(max(
0
)()(
For all x,y in X, where p ≥ 2 is an integer a ≥ o and 0 <c<1 then f and F have unique common fixed point in X.
Example 2.11 [3] Let R be the usual metric space.
Define S, T: R →R by Sx = 2x and Tx = x2
for all x R. Then Sx = Tx for x = 0, 2 but ST0 = TS0, and ST2
≠ TS2. Hence S and T are occasionally weakly compatible self maps but not weakly compatible
Lemma 2.12 [12] Let X be a set, f, g owc self maps of X. If f and g have a unique point of coincidence, w
= fx = gx, then w is the unique common fixed point of f and g.
Lemma 2.13 Let (X,M,*) be a fuzzy metric space. If there exist q (0, 1) such that M (x, y, qt) ≥M (x, y, t) for
all x, y X & t > 0 then x = y
III. MAIN RESULTS:
Theorem 3.1 Let (X,M,*) be a complete fuzzy metric space and let F, G, S and T are self–mapping of X. Let
the pairs {F,S} and {G ,T} be owc . If there exists q ( 0,1) such that
),,(
0
)(
qtGxFxM
dtt
),,(),,(),,(),,(),,,(),,,(min(
0
)(
tSyTxMtSxGyMtTyFxMtGyTyMtFxSxMtTySxM
dtt
for all x, y X and for all t > 0, then there exists a unique point w X such that Fw = Sw = w and a unique
point z X such that Gz = Tz = z Moreover , z = w , so that there is a unique common fixed point of F,G,S and
T.
Proof: Let the pairs { F,S} and { G ,T} be owc so there are points x,y X such that Fx = Sx=Tx and
Gy = Ty=Sy. We claim that Fx = Gy. If not by inequality
),,(
0
)(
qtGxFxM
dtt
),,(),,(),,(),,(),,,(),,,(min(
0
)(
tSyTxMtSxGyMtTyFxMtGyTyMtFxSxMtTySxM
dtt
=
),,(),,,(),,,(),,,(),,,(),,,(min(
0
)(tGyFxMtGyFxMtGyFxMtGyGyMtFxFxMtGyFxM dtt
=
),,(
0
)(
tGyFxM
dtt
4. New results on Occasionally Weakly Compatible Mappingsand…
10
Therefore Fx = Gy , i.e. Fx = Sx = Gy =Ty.=Sy=Tx Suppose that z such that Fz = Sz then by (1) we have Fz =
Sz =Gy = Ty so Fx = Fz and w = Fx = Sx is the unique point of coincidence of F and S.
Similarly there is a unique point z X such that z = Gz = Tz.
Assume that w ≠ z .We have
),,(
0
),,(
0
)()(
qtZWM qtGzFwM
dttdtt
),,(),,,(),,,(),,(),,,(),,,(min(
0
)(
tTzSwMtSwGzMtTzFwMtTzGzMtFzSwMtTzSwM
dtt
=
),,(),,,(),,,(),,(),,,(),,,(min(
0
)(tzwMtwzMtzwMtzzMtzwMtzwM dtt
=
),,(
0
)(
tzwM
dtt
Therefore we have z = w by Lemma 2.14 and z is a common fixed point of F, G, S and T. The uniqueness of
fixed point holds from (3.1)
Theorem3.2: Let (X,M,*) be complete fuzzy metric space and let F,G,S and T be self mappings of X .let the
pairs {F,S} and{G,T} be owc . If there exists q (0,1) such that
),,(
0
)(
qtGyFxM
dtt
)),,(),,,(),,,(),,(),,,((min(
0
)(
tSxGyMtTyFxMtTyGyMtFxSxMtTySxM
dtt
for all x , y X and Ø:[0,1]—› [0,1] such that Ø(t) > t for all 0 < t < 1 ,then there exist a unique common
fixed point of F, G,S and T
Proof: From equation (3.2)
),,(
0
)(
qtGyFxM
dtt
))),,(),.,(),,,(),,,(),,,((min(
0
)(
tSxGymTtYfXMtTyGyMtFxSxMtTySxM
dtt
≥
),,((
0
)(
tGyFxM
dtt
Theorem3.3: Let (X,M,*) be a complete fuzzy metric space and let F,G,S and T are self mappings of X.
Let the pairs {F,S}and {G,T} be owc . If there exists q ( 0,1) such that
),,(
0
)(
qtGyFxM
dtt
)),,(),,,(),,,(),,(),,,((min(
0
)(
tSxGyMtTyFxMtTyGyMtFxSxMtTySxM
dtt
for all x, y X and Ø: (0,1)4
→(0,1) such that Ø (t,1,t,t) > t for all ,0 < t < 1 then there exists a unique
common fixed point of F,G,S and T.
5. New results on Occasionally Weakly Compatible Mappingsand…
11
Proof: Let the pairs {F,S}and {G,T} are owc ,there are points x, y X such that Fx = Sx and Gy = Ty are
Claim that Fx = Gy. By inequality (3.3) we have
),,(
0
)(
qtGyFxM
dtt
)),,(),,,(),,,(),,(),,,((min(
0
)(
tSxGyMtTyFxMtTyGyMtFxSxMtTySxM
dtt
=
),,,(),,,(),,,(),,,(),,,((min((
0
)(
tFxGyMtGyFxMtGyGyMtFxFxMtGyFxMM
dtt
=
),,(),,,(,1.1).,,((
0
)(
tFxGyMtGyFxMtGyFxM
dtt
[∵ M(Fx,Fx,t)=1,M(Gy,Gy,t) =1]
>
),,(
0
)(
tGyFxM
dtt
a contradiction , therefore Fx = Gy i.e. Fx = Sx = Gy = Ty suppose that there is another point z such that Fz = Sz
then by (3.3) we have Fz = Sz = Gy = Ty so Fx = Fz and w = Fx = Tx is unique point of coincidence of F and T.
By Lemma 2.14 w is a unique common fixed point of F and S, similarly there is a unique point z X such
that z = Gz = Tz..Thus z is common fixed point of F,G,S and T. The uniqueness of fixed point holds from (3.3)
Theorem3.4: Let (X,M,*) be complete fuzzy metric space and let F,G,S and T be self mappings of X, let the
pairs {F,S} and {G,T} are owc. If there exists a points q (0,1) for all x, y X and t > 0
),,(
0
)(
qtGyFxM
dtt
),,(),,(),,,(),,,(
0
)(
tTyFxMtTyGyMtSxFxMtTySxM
dtt (3.4)
then there exists a unique common fixed points of F,G ,S and T.
Proof: Let the points {F, S} and {G,T} are owc and there are points x , y X such that Fx = Sx and Gy = Ty
and claim that Fx = Gy By inequality (3.4) We have
),,(
0
)(
qtGyFxM
dtt
),,(),,(),,,(),,,(
0
)(
tTyFxMtTyGyMtSxFxMtTySxM
dtt
=
),,(),,,(),,,(),,,(
0
)(
tGyFxMtGyGyMtFxFxMtGyFxM
dtt
≥
),,(1,1),,,(
0
)(
tGyFxMtGyFxM
dtt
≥
),,(
0
)(
tGyFxM
dtt
Thus we have Fx = Gy i.e. Fx = Sx = Gy = Ty suppose that there is another point z such that Fz=Sz then by (3) we have Fz =
Sz = Gy = Ty so Fx = Fz and w = Fx = Sx is unique point of coincidence of F and S.
Similarly there is a unique point z__ X such that z = Gz = Tz. Thus w is a common fixed point of F,G ,S, and T.
Corollary3.5:Let (X,M,*) be a complete fuzzy metric space and let F,G,S and T be self mapping of X
Let the pairs {F,S} and {G,T} are owc. If there exists a point q (0,1) for all x, y X and t > 0
6. New results on Occasionally Weakly Compatible Mappingsand…
12
),,(
0
)(
qtGyFxM
dtt
),,()2,,(),,,(),,,(),,,(
0
)(
tTyFxMtSxGyMtTyGyMtSxFxMtTySxM
dtt
(3.5)
then there exists a unique common fixed point of F,G,S and T.
Proof: We have
),,(
0
)(
qtGyFxM
dtt
),,()2,,(),,,(),,,(),,,(
0
)(
tTyFxMtSxGyMtTyGyMtSxFxMtTySxM
dtt
),,(),,,(),,(),,,(),,,(),,,(
0
)(
tTyFxMtGyTyMtTySxMtTyGyMtSxFxMtTySxM
dtt
≥
),,(),,,(),,(),,,(),,,(),,,(
0
)(
tTyFxMtGyGyMtTySxMtTyGyMtFxFxMtTySxM
dtt
≥
),,(,1),,(,1,1),,,(
0
)(
tTyFxMtTySxMtTySxM
dtt
≥
),,(),,,(,),,,(
0
)(
tTyFxMtTySxMtTySxM
dtt
i.e. Fx = Sx and Gy = Ty]
and therefore from Theorem 3.2.3 , F, G, S and T have common fixed point.
Corollary3.2.5: Let (X,M,*) be complete fuzzy metric space and let F,G,S and T be self-mapping of X. Let the
pairs {F,S} and {G,T} are owc. If there exist point q (0,1) for all x, y X and t > 0
),,(
0
)(
qtGyFxM
dtt
),,(
0
)(
tTySxM
dtt
then there exists a unique common fixed point of F,G,S and T.
Proof: The proof follows from Corollary 3.2.4
Theorem 3.6: Let (X,M,*) be complete fuzzy metric space . Then continues self mappings S and T of X have
a common fixed point in X if and only if there exists a self mapping F of X such that the following conditions
are satisfied
(i) FX TX SX
(ii) pairs { F,S} and {F,T} are weakly compatible,
(iii) there exists a point q (0,1) such that for every
x, y X and t > 0
),,(
0
)(
qtGyFxM
dtt
),,(),,,(),,,(),,,(
0
)(
tTyFxMtTyFyMtSxFxMtTySxM
dtt
then F, S and T have a unique common fixed point.
Proof: Since compatible implies owc, the result follows from (Theorem3.2.3)
7. New results on Occasionally Weakly Compatible Mappingsand…
13
Theorem 3.7: Let (X,M,*) be a complete fuzzy metric space and let F and G be self mapping of X .Let F and
G are owc. If there exists a point q (0,1) for all x, y X and t > 0
),,(
0
)(
qtSySxM
dtt
),,(),,,(),,,(min(),,,(
0
)(
tFySyMtFxSxMtFyFxMtFyFxM
dtt
for all x,y X , where , , > 0 , + >1. Then F and S have a unique common fixed point.
Proof: Let the pairs {F,S}be owc, so there is a point x X such that Fx = Sx. Suppose that there exist
another point y X for which Fy = Sy We claim that Sx = Sy by equation (8) we have
),,(
0
)(qtSySxM dtt
),,(),,,(),,,(min(),,,(
0
)(
tFySyMtFxSxMtFyFxMtFyFxM
dtt
),,(),,,(),,,(min(),,,(
0
)(
tSySyMtSxSxMtSySxMtSySxM
dtt
=
),,()(
0
)(
tSySxM
dtt
A contradiction, since ( + ) > 1therefore Sx = Sy. Therefore Fx = Fy and Fx is unique.
From lemma 2.14, F and S have a unique fixed point.
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