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Fixed points in fuzzy metric spaces. (English) Zbl 0664.54032
{\it I. Kramosil} and {\it J. Michálek} [Kybernetika 11, 336-344 (1975; Zbl 0319.54002)] extended the concept of probabilistic metric spaces to fuzzy metric spaces. In this context, the author gives fuzzy versions of the Banach contraction principle and of the well-known fixed point theorem of {\it M. Edelstein} [J. Lond. Math. Soc. 37, 74-79 (1962; Zbl 0113.165)].
Reviewer: S.Sessa

MSC:
54H25Fixed-point and coincidence theorems in topological spaces
54A40Fuzzy topology
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References:
[1] Zi-Ke, Deng: Fuzzy pseudo metric spaces. J. math. Anal. appl. 86, 74-95 (1982)
[2] Edelstein, M.: On fixed and periodic points under contractive mappings. J. London math. Soc. 37, 74-79 (1962) · Zbl 0113.16503
[3] Erceg, M. A.: Metric spaces in fuzzy set theory. J. math. Anal. appl. 69, 205-230 (1979) · Zbl 0409.54007
[4] Kaleva, O.; Seikkala, S.: On fuzzy metric spaces. Fuzzy sets and systems 12, 215-229 (1984) · Zbl 0558.54003
[5] Kramosil, J.; Michalek, J.: Fuzzy metric and statistical metric spaces. Kybernetika 11, 334-336 (1975) · Zbl 0319.54002
[6] Kubiak, T.: A topological version of a coincidence theorem. (1981)
[7] Ray, B. K.; Chatterjee, H.: Some results on fixed points in metric and Banach spaces. Bull. acad. Polon. math. 25, 1243-1247 (1977) · Zbl 0396.54039
[8] Schweizer, B.; Sklar, A.: Statistical metric spaces. Pacific J. Math. 10, 314-334 (1960) · Zbl 0091.29801