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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 {\it V. Gregori} and {\it 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 [{\it V. Gregori, S. Romaguera} and {\it P. Veeramani}, Chaos Solitons Fractals 28, No. 4, 902--905 (2006; Zbl 1096.54003)], [{\it D. Miheţ}, Fixed Point Theory Appl. 2007, Article ID 87471, 5 p. (2007; Zbl 1152.54008)], [{\it L. B. Ćirić, S. N. Ješić} and {\it J. S. Ume}, Chaos Solitons Fractals 37, No. 3, 781--791 (2008; Zbl 1137.54326)].

##### MSC:
 54H25 Fixed-point and coincidence theorems in topological spaces 03E72 Fuzzy set theory 54A40 Fuzzy topology
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##### References:
 [1] Atanassov K. Intuitionistic fuzzy sets. In: Sgurev V, editor. VII ITKR’s Session, Sofia June, 1983 Control Sci. and Tech. Library, Bulg. Academy of Sciences, 1984. [2] Atanassov, K.: Intuitionistic fuzzy sets. Fuzzy set syst 20, 87-96 (1986) · Zbl 0631.03040 [3] Atanassov, K.: New operations defined over the intuitionistic fuzzy sets. Fuzzy set syst 61, 137-142 (1994) · Zbl 0824.04004 [4] El Naschie, M. S.: On the uncertainty of Cantorian geometry and two-slit experiment. Chaos, solitons & fractals 9, 517-529 (1998) · Zbl 0935.81009 [5] El Naschie, M. S.: On the verifications of heterotic string theory and &z.epsiv;$(\infty )$ theory. Chaos, solitons & fractals 11, 397-407 (2000) [6] El Naschie, M. S.: On a fuzzy Kähler-like manifold which is consistent with the two slit experiment. Int J nonlinear sci numer simulat 6, 517-529 (2005) [7] El Naschie, M. S.: A review of E-infinity theory and the mass spectrum of high energy particle physics. Chaos, solitons & fractals 19, 209-236 (2004) · Zbl 1071.81501 [8] George, A.; Veeramani, P.: On some results in fuzzy metric spaces. Fuzzy set syst 64, 395-399 (1994) · Zbl 0843.54014 [9] Ghaemi MB, Razani A. Fixed and periodic points in the probabilistic normed and metric spaces. Chaos, Solitons & Fractals, in press, doi:10.1016/j.chaos.2005.08.192. [10] Park, J. H.: Intuitionistc fuzzy metric spaces. Chaos, solitons & fractals 22, 1039-1046 (2004) · Zbl 1060.54010 [11] Razani A. A contraction theorem in fuzzy metric spaces. Fixed Point Theory Applications 2005;3:257 -- 65. · Zbl 1102.54005 [12] Razani A. A fixed point theorem in the Menger probabilistic metric space. New Zealand J Math, to appear. · Zbl 1130.47061 [13] Rodrígues-López, J.; Romaguera, S.: The Hausdorff fuzzy metric on compact sets. Fuzzy set syst 147, 273-283 (2004) · Zbl 1069.54009 [14] Sadati, R.; Park, J. H.: On the intuitionistc fuzzy topological spaces. Chaos, solitons & fractals 27, 331-344 (2006) [15] Schweizer, B.; Sklar, A.: Statistical metric spaces. Pacific J math 10, 314-334 (1960) · Zbl 0091.29801