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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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