×

A common fixed point theorem in fuzzy metric spaces. (English) Zbl 0867.54017

Summary: In this note Jungck’s common fixed point theorem is generalized to fuzzy metric spaces. M. Grabiec [Fuzzy Sets Syst. 27, 385-389 (1988; Zbl 0664.54032)] proved the contraction principle in the setting of fuzzy metric spaces introduced by I. Kramosil and J. Michálek [Kybernetica, Praha 11, 336-344 (1975; Zbl 0319.54002)]. This note offers a generalization of G. Jungck’s theorem [Am. Math. Mon. 83, 261-263 (1976; Zbl 0321.54025)] in the setting of a fuzzy metric space.

MSC:

54A40 Fuzzy topology
54H25 Fixed-point and coincidence theorems (topological aspects)
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] A. George and P. Veeramani, Some results in fuzzy metric space. Fuzzy Sets and Systems; A. George and P. Veeramani, Some results in fuzzy metric space. Fuzzy Sets and Systems · Zbl 0843.54014
[2] Grabiec, M., Fixed points in fuzzy metric spaces, Fuzzy Sets and Systems, 27, 385-389 (1983) · Zbl 0664.54032
[3] Jungck, G., Commutating maps and fixed points, Amer. Math. Monthly, 83, 261-263 (1976) · Zbl 0321.54025
[4] Jungck, G., Compatible mappings and common fixed points, Int. J. Math. Math. Sci., 9, 771-774 (1986) · Zbl 0613.54029
[5] Kramosil, J.; Michalek, J., Fuzzy metric and statistical metric spaces, Kybernetica, 11, 330-334 (1975), (The author did not have to access to this paper.)
[6] Schweizer, B.; Sklar, A., Probabilistic Metric Spaces (1983), North-Holland: North-Holland Amsterdam · Zbl 0546.60010
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.