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On fuzzy \(\varepsilon \)-contractive mappings in fuzzy metric spaces. (English) Zbl 1152.54008

In this paper, the author answers affirmatively the open question raised by A. Razani [Fixed Point Theory Appl. 2005, No. 3, 257–265 (2005; Zbl 1102.54005)]. The author replaces the continuous t-norm \(*\) defined as \(a * b = \min \{a, b\}\) by an arbitrary t-norm. Separation axioms for a fuzzy metric space in the sense of George and Veeramani are used to prove the main results.

MSC:

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

Citations:

Zbl 1102.54005
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References:

[1] George A, Veeramani P: On some results in fuzzy metric spaces.Fuzzy Sets and Systems 1994,64(3):395-399. 10.1016/0165-0114(94)90162-7 · Zbl 0843.54014 · doi:10.1016/0165-0114(94)90162-7
[2] Gregori V, Romaguera S: Characterizing completable fuzzy metric spaces.Fuzzy Sets and Systems 2004,144(3):411-420. 10.1016/S0165-0114(03)00161-1 · Zbl 1057.54010 · doi:10.1016/S0165-0114(03)00161-1
[3] Razani A: A contraction theorem in fuzzy metric spaces.Fixed Point Theory and Applications 2005,2005(3):257-265. 10.1155/FPTA.2005.257 · Zbl 1102.54005 · doi:10.1155/FPTA.2005.257
[4] Grabiec M: Fixed points in fuzzy metric spaces.Fuzzy Sets and Systems 1988,27(3):385-389. 10.1016/0165-0114(88)90064-4 · Zbl 0664.54032 · doi:10.1016/0165-0114(88)90064-4
[5] Schweizer B, Sklar A: Probabilistic Metric Spaces, North-Holland Series in Probability and Applied Mathematics. North-Holland, New York, NY, USA; 1983:xvi+275. · Zbl 0546.60010
[6] Radu V: Some suitable metrics on fuzzy metric spaces.Fixed Point Theory 2004,5(2):323-347. · Zbl 1071.54016
[7] Ćirić L, Ješić S, Ume JS: The existence theorems for fixed and periodic points of nonexpansive mappings in intuitionistic fuzzy metric spaces. to appear in Chaos, Solitons & Fractals · Zbl 1137.54326
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