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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)
##### Keywords:
contraction principle; fuzzy metric space
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##### References:
 [1] A. George and P. Veeramani, Some results in fuzzy metric space. Fuzzy Sets and Systems. To appear. · 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 Amsterdam · Zbl 0546.60010
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