FUZZY FIXED POINTS OF FUZZY MAPPINGS VIA A RATIONAL INEQUALITY

Year 2011, Volume: 40 Issue: 3, 421 - 431, 01.03.2011

Akbar Azam

Abstract

We establish the existence of common fuzzy fixed points for fuzzy mappings under a rational contractive condition on a metric space in connection with the Hausdorff metric on the family of fuzzy sets, and apply it to obtain common fixed points of fuzzy (multivalued) mappings satisfying a rational contractive condition associated with the d∞ (Hausdorff) metric.

Keywords

Fixed point, Common fixed point, Contractive type mapping, fuzzy mapping, 2000 AMS Classification: 46 S 40

FUZZY FIXED POINTS OF FUZZY MAPPINGS VIA A RATIONAL INEQUALITY

Abstract

References

• Abu-Donia, H. M. Common fixed points theorems for fuzzy mappings in metric spaces under ϕ contraction condition, Chaos, Solitons & Fractals 34, 538–543, 2007.
• Arora, S. C. and Sharma, V. Fixed points for fuzzy mappings, Fuzzy Sets and Systems 110, 127–130, 2000.
• Azam, A. and Arshad, M. A note on “fixed point theorems for fuzzy mappings” by P. Vijayaraju and M. Marudai, Fuzzy Sets and Systems 161, 1145–1149, 2010.
• Azam, A., Arshad, M. and Vetro, P. On a pair of fuzzy -6 c contractive mappings, Math. Comp. Modelling 52, 207–214, 2010. [5] Azam, A. and Beg, I. Common fixed points of fuzzy maps, Math. Comp. Modelling 49, 1331–1336, 2009.
• Azam, A., Arshad, M. and Beg, I. Fixed points of fuzzy contractive and fuzzy locally con- tractive maps, Chaos, Solitons & Fractals 42 (5), 2836–2841, 2009.
• Beg, I. and Azam, A. Fixed points of asymptotically regular multivalued mappings, J. Aus- tral. Math. Soc. (Series A) 53, 313–226, 1992.
• Bose, R. K. and Sahani, D. Fuzzy mappings and fixed point theorems, Fuzzy Sets and Systems 21, 53–58, 1987.
• Butnariu, D. Fixed point for fuzzy mapping, Fuzzy Sets and Systems 7, 191–207, 1982.
• Cho, Y. J., Fisher, B. and Ganga, G. S. Coincidence theorems for nonlinear hybird contrac- tions, Internat. J. Math. & Math. Sci. 20, 249–256, 1997.
• Edelstein, M. An extension of Banach’s contraction principle, Proc. Amer. Math. Soc 12, 7–10, 1961.
• Edelstein, M. On fixed and periodic points under contractive mappings, J. London Math. Soc 37, 74–79, 1962.
• El-Naschie, M. S. On the unification of the fundamental forces and complex time in the ε
• ∞-space, Chaos, Solitons & Fractals 11, 1149–1162, 2000.
• El-Naschie, M. S. On an eleven dimensional ε∞fractal space time theory, Int. J. Nonlinear Sci. Numer. Simul. 7, 407–409, 2006. [15] Fisher, B. Theorems on mappings satisfying a rational inequality, Comment. Math. univ. Caroline 19, 37–44, 1978.
• Flores, H. R., Franulic, A. F., Medar, M. R. and Bassanezi, R. C. Stability of fixed points set of fuzzy contractions, Appl.Math. Lett. 4, 33–37, 1998.
• Heilpern, S. Fuzzy mappings and fixed point theorems, J. Math. Anal. Appl. 83, 566–569, 1981.
• Kamran, T. Common fixed points theorems for fuzzy mappings, Chaos Solitons and Fractals 38, 1378–1382, 2008.
• Lee, B. S. and Cho, S. J. A fixed point theorem for contractive type fuzzy mappings, Fuzzy Sets and Systems 61, 309–312, 1994. [20] Lee, B. S., Sung, G. M., Cho, S. J. and Kim, D. S. A common fixed point theorem for a pair of fuzzy mappings, Fuzzy Sets and Systems 98, 133–136, 1998.
• Nadler, S. B. Multivalued contraction mappings, Pacific J. Math. 30, 475–488, 1969.
• Park, J. Y. and Jeong, J. U. Fixed point theorems for fuzzy mappings, Fuzzy Sets and Sys- tems 87, 111–116, 1997.
• Weiss, M. D. Fixed points and induced fuzzy topologies for fuzzy sets, J. Math. Anal. Appl. 50, 142–150, 1975.