Abstract

The present study introduce the notion of weak compatibility and E. A. property for mixed g-monotone mappings in setting of intuitionistic fuzzy metric space and utilize these perceptions to prove a coupled fixed point theorem for such nonlinear contractive mappings. More to the point together with several recent developments, the efforts of this work can be used to explore a large category of problems. An example is also established for the support of our result.

References

• Aamri, M. , El Moutawakil, D. 1988. Some new common fixed point theorems under strict contractive conditions, Journal of Mathematical Analysis and Applications 226(1988) 251-258.
• Alaca, C. , Turkoglu D. and Yildiz, C. 2006. Fixed point in intuitionistic fuzzy metric spaces, Chaos, Solitons & Fractals 29(2006) 1073-1078.
• Alaca, C. , Altun, I. and Turkoglu, D. 1986. On compatible mapping of type (I) and (II) in intuitionistic fuzzy metric spaces, Korean Mathematical Society 23(3) (1986) 771-779.
• Atanssove, K. 1986. Intuitionstic fuzzy sets, Fuzzy Sets and Systems 2(1) (1986) 87-96.
• Gana Bhaskar, T. and Lakshmikantham, V. 2006. Fixed point theorems in partially ordered metric space and applications, Nonlinear Analysis 65 (2006) 1379-1393.
• Choudhary, B. S. and Kundu, A. 2010. A coupled coincidence point result in partially ordered metric space for compatible mappings, Nonlinear Analysis 73 (2010) 2524-2531.
• Ciric, L. , and Lakshmikantham, V. 2009. Coupled random fixed point theorems in partially ordered metric spaces, Stoch. Analysis. 27(6) (2009) 1246-1259.
• Dubois, D. , and Prade, H. 1980. Fuzzy sets theory and applications to policy analysis and information systems, New York, Plenum Press (1980).
• Grabiec, M. 1988. Fixed points in fuzzy metric spaces. Fuzzy Sets and Systems 27(1988) 385-389.
• Gregori, V. , Romaguera, S. and Veeramani, P. 2006. A note on intuitionistic fuzzy metric spaces, Chaos, Solitons & Fractals 28(4) (2006) 902-905.
• Hadzic, O. and Pap, E. 2001. Fixed point theory in PM-spaces, Dordrecht: Kluwer Academic publishers, (2001).
• Kaleva, O. and Seikkala, S. 1984. On fuzzy metric spaces. Fuzzy Sets and Systems 12(1984) 215-229.
• Klement, EP, Mesiar, R. and Pap, E. 2000. Triangular norms, trends in logic & Dordrecht, Kluwer Academic Publishers (2000).
• Kramosil, O. and Michalek, J. 1975. Fuzzy metrics and statistical metric spaces, Kybernetika 15(1975) 326-334.
• Kumar, S. , Vats, R. K. , Singh, V. and Garg, S. K. 2010. Some common fixed point theorem in intuitionstic fuzzy metric spaces, Int. Journal of Math. Analysis, 26 (4) (2010), 1255-1270.
• Lakshmikantham, V. and Ciric, L. 2009. Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Analysis 70 (12) (2009) 4341-4349.
• Menger, K. 1942. Statistical metrics, Proceeding of National Academy Science 28(1942) 535–537.
• Mihet, D. 2010. Fixed point theorem in fuzzy metric spaces using property E. A. , Nonlinear Anal. 73 (2010) 2184-2188.
• Naschie, M. S. El 2007. A review of applications and results of E-infinity theory, International Journal of Nonlinear Sciences and Numerical Simulation, 8(1) (2007) 11-20.
• Naschie, M. S. El 2004. A review of E-infinity theory and the mass spectrum of high energy particle physics. Chaos Solitons & Fractals 19(1) (2004) 209-236.
• Naschie, M. S. El 2005. On a class of fuzzy Kahler-like manifolds. Chaos Solitons & Fractals 26(2) (2005) 257-261.
• Naschie, M. S. El 2005. From experimental quantum optics to quantum gravity via a fuzzy Kahler manifold, Chaos, Solitons & Fractals 25(5) (2005) 969-977.
• Naschie, M. S. El 1998. On the uncertainty of Cantorian geometry and the two slit experiment. Chaos, Solitons & Fractals 9(3) (1998) 517-529.
• Naschie, M. S. El 2004. Quantum gravity, Clifford algebras, fuzzy set theory and the fundamental constants of nature, Chaos, Solitons & Fractals 20(3) (2004) 437-450.
• Pant, R. P. 1999. R-weak commutatibility and common fixed points, Soochow Journal Math 25(1999) 37-42.
• Park, J. H. 2004. Intuitionistic fuzzy metric spaces, Chaos Solitons & Fractals 22(2004) 1039-1046.
• Park, J. H. , Park, J. S. and Kwun, Y. C. 2005. A common fixed point theorem in intuitionstic fuzzy metric spaces, In: Advance in Natural Computing Data Mining (Proceeding 2nd ICNC and 3rd FSKK) (2005) 293-300.
• Park, J. S. and Kwun, Y. C. and Park, J. H. 2006. Compatible mapping and compatible mapping of type (?) and (?) in intuitionistic fuzzy metric spaces, Demonstration Mathematica 39(3) (2006) 671-684.
• Romaguera, S. and Tirado, P. 2009. Contraction maps on Ifqm-spaces with application to recurrence equation of quicksort, Electronics Notes in Theoretical Computer 225(2009) 269-279.
• Saadati, R. and Park, J. H. 2006. On the intuitionistic fuzzy topological spaces, Chaos, Solitons & Fractals 27(2) (2006) 331-344.
• Schweizer, B. and Sklar, A. 1983. Probabilistic metric spaces, Amesterdam North Holland 1983.
• Schweizer, B. and Sklar, A. 1983. Probabilistic metric spaces, Amesterdam North Holland 1983.
• Turkoglu, D. , Alaca, C. , Cho, Y. J. and C. Yildiz, 2006. Common fixed point theorem in intuitionistic fuzzy metric spaces, Journal of applied mathematics and computing, 22(1-2) (2006) 411-424.
• Zadeh, L. A. 1965. Fuzzy Sets, Information and control 8(1965) 103-112.
• Sabetghadam, F. , Masiha, H. P. and Sanatpour, A. H. 2009. Some coupled fixed point theorem in cone metric spaces, Fixed Point Theory Appl. 2009, Art. ID 125426, 8 pp.
• Samet, B. 2010. Coupled fixed point theorem for generalized Meir-Keeler contaction in partially ordered metric space, Nonlinear Anal. , 72 (12) (2010) 4508-45017.