Existence of fixed point for the nonexpansive mapping of intuitionistic fuzzy metric spaces
The existence of a fixed point of an intuitionistic fuzzy nonexpansive mapping is proved. The theorem generalizes a result of \textit{V. Gregori} and \textit{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 [\textit{V. Gregori, S. Romaguera} and \textit{P. Veeramani}, Chaos Solitons Fractals 28, No. 4, 902--905 (2006; Zbl 1096.54003)], [\textit{D. Miheţ}, Fixed Point Theory Appl. 2007, Article ID 87471, 5 p. (2007; Zbl 1152.54008)], [\textit{L. B. Ćirić, S. N. Ješić} and \textit{J. S. Ume}, Chaos Solitons Fractals 37, No. 3, 781--791 (2008; Zbl 1137.54326)].
scientific article; zbMATH DE number 5285337