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Impact of common property (E.A.) on fixed point theorems in fuzzy metric spaces. (English) Zbl 1214.54034

Summary: We observe that the notion of common property (E.A.) relaxes the required containment of range of one mapping into the range of others which is utilized to construct the sequence of joint iterates. As a consequence, a multitude of recent fixed point theorems of the existing literature are sharpened and enriched.

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
54A40 Fuzzy topology
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References:

[1] Zadeh LA: Fuzzy sets.Information and Computation 1965, 8: 338-353. · Zbl 0139.24606
[2] Turkoglu D, Rhoades BE: A fixed fuzzy point for fuzzy mapping in complete metric spaces.Mathematical Communications 2005,10(2):115-121. · Zbl 1089.54518
[3] Deng Z: Fuzzy pseudometric spaces.Journal of Mathematical Analysis and Applications 1982,86(1):74-95. 10.1016/0022-247X(82)90255-4 · Zbl 0501.54003 · doi:10.1016/0022-247X(82)90255-4
[4] Kaleva O, Seikkala S: On fuzzy metric spaces.Fuzzy Sets and Systems 1984,12(3):215-229. 10.1016/0165-0114(84)90069-1 · Zbl 0558.54003 · doi:10.1016/0165-0114(84)90069-1
[5] George A, Veeramani P: On some results of analysis for fuzzy metric spaces.Fuzzy Sets and Systems 1997,90(3):365-368. 10.1016/S0165-0114(96)00207-2 · Zbl 0917.54010 · doi:10.1016/S0165-0114(96)00207-2
[6] Kramosil I, Michálek J: Fuzzy metrics and statistical metric spaces.Kybernetika 1975,11(5):336-344. · Zbl 0319.54002
[7] El Naschie MS: On a fuzzy khaler-like manifold which is consistent with two slit experiment.International Journal of Nonlinear Sciences and Numerical Simulation 2005, 6: 95-98. 10.1515/IJNSNS.2005.6.2.95 · Zbl 06942101 · doi:10.1515/IJNSNS.2005.6.2.95
[8] Mihet D: A generalization of a contraction principle in probabilistic metric spaces (II).International Journal of Mathematics and Mathematical Sciences 2005, 2005: 729-736. 10.1155/IJMMS.2005.729 · Zbl 1083.54535 · doi:10.1155/IJMMS.2005.729
[9] Mihet D: Fixed point theorems in fuzzy metric spaces using property E.A.Nonlinear Analysis 2010, 73: 2184-2188. 10.1016/j.na.2010.05.044 · Zbl 1195.54082 · doi:10.1016/j.na.2010.05.044
[10] Abbas M, Altun I, Gopal D: Common fixed point theorems for non compatible mappings in fuzzy metric spaces.Bulletin of Mathematical Analysis and Applications 2009,1(2):47-56. · Zbl 1175.54048
[11] Imdad M, Ali J: Some common fixed point theorems in fuzzy metric spaces.Mathematical Communications 2006,11(2):153-163. · Zbl 1152.54355
[12] Pant V: Contractive conditions and common fixed points in fuzzy metric space.Journal of Fuzzy Mathematics 2006,14(2):267-272. · Zbl 1103.54307
[13] Singh B, Chauhan MS: Common fixed points of compatible maps in fuzzy metric spaces.Fuzzy Sets and Systems 2000,115(3):471-475. 10.1016/S0165-0114(98)00099-2 · Zbl 0985.54009 · doi:10.1016/S0165-0114(98)00099-2
[14] Singh B, Jain S: Semicompatibility and fixed point theorems in fuzzy metric space using implicit relation.International Journal of Mathematics and Mathematical Sciences 2005, (16):2617-2629. · Zbl 1087.54506
[15] Vetro C, Vetro P: Common fixed points for discontinuous mappings in fuzzy metric spaces.Rendiconti del Circolo Matematico di Palermo 2008,57(2):295-303. 10.1007/s12215-008-0022-7 · Zbl 1165.54313 · doi:10.1007/s12215-008-0022-7
[16] Jungck G: Commuting mappings and fixed points.The American Mathematical Monthly 1976,83(4):261-263. 10.2307/2318216 · Zbl 0321.54025 · doi:10.2307/2318216
[17] Singh B, Jain S: Weak-compatibility and fixed point theorems in fuzzy metric space.Ganita 2005,56(2):167-176. · Zbl 1211.54066
[18] Vasuki R: Common fixed points for -weakly commuting maps in fuzzy metric spaces.Indian Journal of Pure and Applied Mathematics 1999,30(4):419-423. · Zbl 0924.54010
[19] Sessa S: On a weak commutativity condition of mappings in fixed point considerations.Publications de l’Institut Mathématique 1982, 32(46): 149-153. · Zbl 0523.54030
[20] Jungck G: Compatible mappings and common fixed points.International Journal of Mathematics and Mathematical Sciences 1986,9(4):771-779. 10.1155/S0161171286000935 · Zbl 0613.54029 · doi:10.1155/S0161171286000935
[21] Murthy PP: Important tools and possible applications of metric fixed point theory.Nonlinear Analysis: Theory, Methods & Applications 2001,47(5):3479-3490. 10.1016/S0362-546X(01)00465-5 · Zbl 1042.54507 · doi:10.1016/S0362-546X(01)00465-5
[22] Aamri M, El Moutawakil D: Some new common fixed point theorems under strict contractive conditions.Journal of Mathematical Analysis and Applications 2002,270(1):181-188. 10.1016/S0022-247X(02)00059-8 · Zbl 1008.54030 · doi:10.1016/S0022-247X(02)00059-8
[23] Imdad M, Ali J: A general fixed point theorem in fuzzy metric spaces via an implicit function.Journal of Applied Mathematics & Informatics 2008, 26: 591-603.
[24] Chugh R, Kumar S: Common fixed point theorem in fuzzy metric spaces.Bulletin of the Calcutta Mathematical Society 2002,94(1):17-22. · Zbl 1065.54512
[25] Turkoglu D, Alaca C, Cho YJ, Yildiz C: Common fixed point theorems in intuitionistic fuzzy metric spaces.Journal of Applied Mathematics & Computing 2006,22(1-2):411-424. 10.1007/BF02896489 · Zbl 1106.54020 · doi:10.1007/BF02896489
[26] Imdad M, Ali J, Tanveer M: Coincidence and common fixed point theorems for nonlinear contractions in Menger PM spaces.Chaos, Solitons & Fractals 2009,42(5):3121-3129. 10.1016/j.chaos.2009.04.017 · Zbl 1198.54076 · doi:10.1016/j.chaos.2009.04.017
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