Common Fixed Point Theorems in a New Fuzzy Metric Space

We generalize the Hausdorff fuzzy metric in the sense of Rodriguez-Lopez and Romaguera, and we introduce a new M ∞ -fuzzy metric, where M ∞ -fuzzy metric can be thought of as the degree of nearness between two fuzzy sets with respect to any positive real number. Moreover, under ϕ -contraction condition, in the fuzzy metric space, we give some common fixed point theorems for fuzzy mappings.

[1]  Azriel Rosenfeld,et al.  Dissimilarity measures between fuzzy sets or fuzzy structures , 2003, Inf. Sci..

[2]  Valentín Gregory,et al.  Some properites of fuzzy metric spaces , 2000 .

[3]  Weiyin Fei,et al.  Existence and uniqueness of solution for fuzzy random differential equations with non-Lipschitz coefficients , 2007, Inf. Sci..

[4]  Fuzzy incidence matrix of fuzzy simplicial complexes and its folding , 2002 .

[5]  Osmo Kaleva,et al.  On fuzzy metric spaces , 1984 .

[6]  Peter E. Kloeden,et al.  Characterization of compact subsets of fuzzy sets , 1989 .

[7]  Jari Kortelainen,et al.  Applying modifiers to knowledge acquisition , 2001, Inf. Sci..

[8]  Gerald Beer,et al.  Topologies on Closed and Closed Convex Sets , 1993 .

[9]  Gabriele H. Greco,et al.  Supremum metric and relatively compact sets of fuzzy sets , 2006 .

[10]  M. Puri,et al.  The Concept of Normality for Fuzzy Random Variables , 1985 .

[11]  Dong Qiu,et al.  Supremum metric on the space of fuzzy sets and common fixed point theorems for fuzzy mappings , 2008, Inf. Sci..

[12]  Dorel Mihet,et al.  Fuzzy psi-contractive mappings in non-Archimedean fuzzy metric spaces , 2008, Fuzzy Sets Syst..

[13]  Gabriele H. Greco.  A characterization of relatively compact sets of fuzzy sets , 2006 .

[14]  G. Debreu.  Integration of correspondences , 1967 .

[15]  A. George,et al.  On some results in fuzzy metric spaces , 1994 .

[16]  Valentín Gregori,et al.  On completion of fuzzy metric spaces , 2002, Fuzzy Sets Syst..

[17]  Phil Diamond,et al.  Absolute retracts and a general fixed point theorem for fuzzy sets , 1997, Fuzzy Sets Syst..

[18]  Dorel Miheţ.  On Fuzzy -Contractive Mappings in Fuzzy Metric Spaces , 2007 .

[19]  Dong Qiu,et al.  Common fixed point theorems for fuzzy mappings under Φ-contraction condition , 2009 .

[20]  Valentín Gregori,et al.  Some properties of fuzzy metric spaces , 2000, Fuzzy Sets Syst..

[21]  M. Puri,et al.  Fuzzy Random Variables , 1986 .

[22]  P. V. Subrahmanyam,et al.  A Common Fixed Point Theorem in Fuzzy Metric Spaces , 1995, Inf. Sci..

[23]  Congxin Wu,et al.  On the completion of fuzzy metric spaces , 2008, Fuzzy Sets Syst..

[24]  J. H. Park.  Intuitionistic Fuzzy Metric Spaces , 2004 .

[25]  M. A. Erceg,et al.  Metric spaces in fuzzy set theory , 1979 .

[26]  Peter E. Kloeden.  Compact supported endographs and fuzzy sets , 1980 .

[27]  Mariusz Grabiec,et al.  Fixed points in fuzzy metric spaces , 1988 .

[28]  Dorel Mihet,et al.  A Banach contraction theorem in fuzzy metric spaces , 2004, Fuzzy Sets Syst..

[29]  H. M. Abu-Donia.  Common fixed point theorems for fuzzy mappings in metric space under ϕ-contraction condition , 2007 .

[30]  Zike Deng,et al.  FUZZY PSEUDO-METRIC SPACES , 1982 .

[31]  H. K. El-Sayied.  Study on generalized convex fuzzy bodies , 2004, Appl. Math. Comput..

[32]  Lotfi A. Zadeh,et al.  Fuzzy Sets , 1996, Inf. Control..

[33]  B. Schweizer,et al.  Statistical metric spaces. , 1960 .

[34]  Salvador Romaguera,et al.  The Hausdor$ fuzzy metric on compact sets , 2004 .

[35]  Osmo Kaleva,et al.  On the convergence of fuzzy sets , 1985 .