A COMMON FIXED POINT THEOREM IN FUZZY METRIC SPACE USING SEMI-COMPATIBLE MAPPINGS

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Dr. V.K. Agarwal

Abstract

 In this paper, the concept of semi-compatibility and weak compatibility in Fuzzy metric space has been applied to prove a common fixed point theorem. We generalize the result of Arihant Jain et.al. [11], using rational inequality.

Keyword: Fuzzy metric space, common fixed point, compatible maps, semi-compatible maps and weak compatible maps.

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How to Cite
Agarwal, D. V. (2015). A COMMON FIXED POINT THEOREM IN FUZZY METRIC SPACE USING SEMI-COMPATIBLE MAPPINGS. Journal of Global Research in Mathematical Archives(JGRMA), 2(8), 01–05. Retrieved from https://jgrma.com/index.php/jgrma/article/view/246
Section
Research Paper

References

. Badard, R., Fixed point theorem for fuzzy numbers, Fuzzy Sets and Systems 13(1984), 291-302.

. Banach, S.:Theorie des Operations Lineaires, Monography, Mathemateyczne, Warszawa,Poland 1932.

. Butnariu, D. : Fixed point theorems for fuzzy mappings, fuzzy sets and systems 7 (1982) , 191-207.

. Deng. Z. K.: Fuzzy pseudo–metric space ,J.Math. Anal.Appl. 86(1982),74-95.

. Erceg, M. A.: Metric spaces in fuzzy set theory J. Math. Anal. Appl. 69(1979) ,205-230.

. Fang, J. X., On fixed point theorem in fuzzy metric spaces ,Fuzzy Sets and Systems 46(1992) ,107-113.

. Fang, J. X., A note on fixed point theorem of Hadzic , Fuzzy Sets and Systems 48(1992) , 391-395.

. George,A. Veeramani, P.,“On some results of analysis for Fuzzy Metric Spacesâ€, Fuzzy Sets and System, 90(1997), 365-368.

. Grabiec, M.,Fixed point in fuzzy metric space , Fuzzy Sets and Systems 27(1988), 385-389.

. Gregori, V. and Sapena, A., On fixed point theorem in fuzzy metric spaces, Fuzzy Sets and Systems 125(2002), 245-252.

Jain A., Badshah V. H. and Prasad S. K., Fixed point theorem in fuzzy metric space for semi-compatible mappings, IJRRAS 12 (3), September 2012, 523-526.

. Kaleva O. and Seikkala S., On fuzzy metric spaces , Fuzzy sets and systems 12(1984), 215-229.

. Kramosil, I. and Michalek J., Fuzzy metric and Statistical metric spaces, Kybernetica 11(1975), 326-334.

. Kumar, S., Common fixed point theorem for minimal commutativity type mappings in Fuzzy metric spaces.Thai Journal of Mathematics,6(2008), 239-270.

. Kumar, S. and Pant, B. D., A Common fixed point theorem for expansion mappings in Probabilistic metric spaces Ganita, 57(2006), 89-95.

. Pap, E.,Hadzic, O. and Mesiar, R., A fixed point theorem in Probabilistic metric spaces and an application, J. Math. Anal. Appl. 202(1996), 433-449.

. Razani, A. and Shirdaryadzi, M., Some results on fixed points in fuzzy metric space, J. Appl.Math. Comp.20(2006), 401-408.

. Schweizer, B. and Sklar, A., Statistical metric spaces, Pacific Journal Math. 10(1960), 313-334.

. Sharma, S., On fuzzy metric space, Southeast Asian Bull. Of Math. 26(2002) 133-145.

. Sharma, S., Common fixed point in fuzzy metric space, Fuzzy sets and systems. 127(2002), 345-352.

. Singh, B. and Jain, S., Semi-compatibility, compatibility and fixed point theorems in fuzzy metric space, Journal of Chungecheong Math. Soc. 18(1), (2005), 1-22.

. Zadeh L. A., Fuzzy sets information and control , 8(1965), 338-353.