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Existence of fixed point for the nonexpansive mapping of intuitionistic fuzzy metric spaces. (English) Zbl 1143.54019
The existence of a fixed point of an intuitionistic fuzzy nonexpansive mapping is proved. The theorem generalizes a result of V. Gregori and A. Sapena [Fuzzy Sets Syst. 125, No. 2, 245–252 (2002; Zbl 0995.54046)]. Also, the Edelstein periodic point theorem for locally contractive mappings is extended from metric spaces to intuitionistic fuzzy metric spaces. For related articles the reader is referred to [V. Gregori, S. Romaguera and P. Veeramani, Chaos Solitons Fractals 28, No. 4, 902–905 (2006; Zbl 1096.54003)], [D. Miheţ, Fixed Point Theory Appl. 2007, Article ID 87471, 5 p. (2007; Zbl 1152.54008)], [L. B. Ćirić, S. N. Ješić and J. S. Ume, Chaos Solitons Fractals 37, No. 3, 781–791 (2008; Zbl 1137.54326)].
MSC:
54H25Fixed-point and coincidence theorems in topological spaces
03E72Fuzzy set theory
54A40Fuzzy topology