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Fixed points in fuzzy metric spaces. (English) Zbl 0664.54032

I. Kramosil and 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 M. Edelstein [J. Lond. Math. Soc. 37, 74-79 (1962; Zbl 0113.165)].
Reviewer: S.Sessa

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
54A40 Fuzzy topology
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References:

[1] Zi-ke, Deng, Fuzzy pseudo metric spaces, J. Math. Anal. Appl., 86, 74-95 (1982) · Zbl 0501.54003
[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
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[5] Kramosil, J.; Michalek, J., Fuzzy metric and statistical metric spaces, Kybernetika, 11, 334-336 (1975) · Zbl 0319.54002
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