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

Grabiec, Mariusz

Fuzzy Sets Syst. 27, No. 3, 385-389 (1988).

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

Keywords:

fuzzy versions of the Banach contraction principle

Citations:

Zbl 0319.54002; Zbl 0113.165

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
[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), Preprint
[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