Fixed points of fuzzy contractive and fuzzy locally contractive maps

Abstract We establish some fixed point theorems for fuzzy contractive and fuzzy locally contractive mappings on a compact metric space with the d ∞ -metric for fuzzy sets. Our results generalized well-known classical results of Edelstein.

[1]  A. Razani,et al.  A contraction theorem in fuzzy metric spaces , 2005 .

[2]  M. S. El Naschie,et al.  On a class of fuzzy Kähler-like manifolds , 2005 .

[3]  C. Waters A fixed point theorem for locally nonexpansive mappings in normed spaces , 1986 .

[4]  Vagisha Sharma,et al.  Fixed point theorems for fuzzy mappings , 2000, Fuzzy Sets Syst..

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

[6]  T. Som,et al.  Some fixed point theorems for fuzzy mappings , 1989 .

[7]  M. S. El Naschie,et al.  On an Eleven Dimensional E-inflnity Fractal Spacetime Theory , 2006 .

[8]  Sung Jin Cho,et al.  A fixed point theorem for contractive-type fuzzy mappings , 1994 .

[9]  S. Nadler Multi-valued contraction mappings. , 1969 .

[10]  Locally contractive and expansive mappings , 1982 .

[11]  Stanisław Heilpern,et al.  Fuzzy mappings and fixed point theorem , 1981 .

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

[13]  Ismat Beg,et al.  Common fixed points of fuzzy maps , 2009, Math. Comput. Model..

[14]  M. E. Naschie,et al.  Wild topology, hyperbolic geometry and fusion algebra of high energy particle physics , 2002 .

[15]  M. Edelstein On Fixed and Periodic Points Under Contractive Mappings , 1962 .

[16]  Tayyab Kamran Common fixed points theorems for fuzzy mappings , 2008 .

[17]  Sehie Park,et al.  Fixed points of $f$-contractive maps , 1978 .

[18]  R. K. Bose,et al.  Fuzzy mappings and fixed point theorems , 1987 .

[19]  Donal O'Regan,et al.  Fuzzy contractive maps and fuzzy fixed points , 2002, Fuzzy Sets Syst..

[20]  Dorel Mihet,et al.  On Fuzzy -Contractive Mappings in Fuzzy Metric Spaces , 2007, Fuzzy Sets Syst..

[21]  M. Edelstein,et al.  An extension of Banach’s contraction principle , 1961 .

[22]  Dan Butnariu,et al.  Fixed points for fuzzy mappings , 1982 .

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

[24]  Muhammad Arshad,et al.  Fixed points of a sequence of locally contractive multivalued maps , 2009, Comput. Math. Appl..

[25]  D. F. Bailey,et al.  Some Theorems on Contractive Mappings , 1966 .

[26]  Evidence of a conspiracy among fixed point theorems , 1975 .

[27]  Fixed points for contractive multifunctions , 1971 .

[28]  L. Ciric Some new results for Banach contractions and Edelstein contractive mappings on fuzzy metric spaces , 2009 .