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On fuzzy contractive mappings in fuzzy metric spaces. (English) Zbl 1117.54008
Fixed point theorems for fuzzy contractive mappings due to V. Gregori and A. Sapena [ibid. 125, No. 2, 245–252 (2002; Zbl 0995.54046)] are extended to Edelstein fuzzy contractive mappings. Convergence properties for fuzzy contractive mappings are studied in fuzzy metric spaces in the sense of A. George and P. Veeramani [ibid. 64, No. 3, 395–399 (1994; Zbl 0843.54014)] and I. Kramosil and J. Michalek [Kybernetika, Praha 11, 336–344 (1975; Zbl 0319.54002)].

##### MSC:
 54A40 Fuzzy topology 54E35 Metric spaces, metrizability 54A05 Topological spaces and generalizations (closure spaces, etc.) 54H25 Fixed-point and coincidence theorems (topological aspects)
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##### References:
 [1] Chang, S.S.; Cho, Y.J.; Kang, S.M., Probabilistic metric spaces and nonlinear operator theory, (1994), Sichuan University Press Chengdu [2] Constantin, Gh.; Istrăţescu, I., Elements of probabilistic analysis with applications, () [3] Egbert, R.J., Products and quotients of probabilistic metric spaces, Pacific J. math., 24, 3, 437-455, (1968) · Zbl 0175.46601 [4] Fang, J.-X., On fixed point theorems in fuzzy metric spaces, Fuzzy sets and systems, 46, 107-113, (1992) · Zbl 0766.54045 [5] George, A.; Veeramani, P., On some results in fuzzy metric spaces, Fuzzy sets and systems, 64, 395-399, (1994) · Zbl 0843.54014 [6] George, A.; Veeramani, P., On some results of analysis for fuzzy metric spaces, Fuzzy sets and systems, 90, 365-368, (1997) · Zbl 0917.54010 [7] Grabiec, M., Fixed points in fuzzy metric spaces, Fuzzy sets and systems, 27, 385-389, (1988) · Zbl 0664.54032 [8] Gregori, V.; Romaguera, S., Some properties of fuzzy metric spaces, Fuzzy sets and systems, 115, 485-489, (2000) · Zbl 0985.54007 [9] Gregori, V.; Romaguera, S., Characterizing completable fuzzy metric spaces, Fuzzy sets and systems, 144, 3, 411-420, (2004) · Zbl 1057.54010 [10] Gregori, V.; Sapena, A., On fixed point theorems in fuzzy metric spaces, Fuzzy sets and systems, 125, 245-253, (2002) · Zbl 0995.54046 [11] Hadžić, O.; Pap, E., Fixed point theory in probabilistic metric spaces, (2001), Kluwer Academic Publishers Dordrecht [12] Höhle, U., Probabilistische metriken auf der menge der nichtnegativen verteilungsfunctionen, Aequationes math., 18, 345-356, (1978) · Zbl 0412.60020 [13] Istrăţescu, I., On some fixed points theorems in generalized Menger spaces, Boll. un. mat. ital. V. ser. A, 13, 95-100, (1976) [14] Kramosil, O.; Michalek, J., Fuzzy metric and statistical metric spaces, Kybernetika, 11, 336-344, (1975) · Zbl 0319.54002 [15] Miheţ, D., A Banach contraction theorem in fuzzy metric spaces, Fuzzy sets and systems, 144, 3, 431-439, (2004) · Zbl 1052.54010 [16] V. Radu, Equicontinuous iterates of t-norms and applications to random normed and fuzzy Menger spaces, in: J. Sousa Ramos, D. Gronau, C. Mira, L. Reich, A.N. Sharkowski (Eds.), Iteration Theory (ECIT 02), Grazer Math. Ber. 33 (2004) 323-350. · Zbl 1058.54021 [17] Radu, V., Some suitable metrics on fuzzy metric spaces, Fixed point theory, 5, 2, 323-347, (2004) · Zbl 1071.54016 [18] A. Razani, A contraction theorem in fuzzy metric spaces, Fixed Point Theory Appl. (3) (2005) 257-265. · Zbl 1102.54005 [19] B. Schweizer, A. Sklar, Probabilistic metric spaces, in: North Holland Series in Probability and Applied Mathematics, New York, Amsterdam, Oxford, 1983 and the new edition in Dover Books on Mathematics, Dover, New York, 2005. [20] Sehgal, V.M.; Bharucha-Reid, A.T., Fixed points of contraction mappings on probabilistic metric spaces, Math. systems theory, 6, 97-104, (1972) · Zbl 0244.60004 [21] Tan, N.X., Generalized probabilistic metric spaces and fixed point theorems, Math. nachr., 129, 205-218, (1986) · Zbl 0603.54049 [22] Vasuki, R.; Veeramani, P., Fixed point theorems and Cauchy sequences in fuzzy metric spaces, Fuzzy sets and systems, 135, 3, 409-413, (2003) · Zbl 1029.54012
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