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Fixed point theorems for cyclic contraction mappings in fuzzy metric spaces. (English) Zbl 1429.54058
Summary: In the present paper, an extension of the Edelstein contraction theorem for cyclic contractions in a fuzzy metric space is established, which also can be considered as a generalization of the fuzzy Edelstein contraction theorem introduced by M. Grabiec [Fuzzy Sets Syst. 27, No. 3, 385–389 (1988; Zbl 0664.54032)]. Additionally, we extend a fixed point theorem in $$G$$-complete fuzzy metric spaces given by Y.-H. Shen et al. [Iran. J. Fuzzy Syst. 10, No. 4, 125–133 (2013; Zbl 1333.54050)] to $$M$$-complete fuzzy metric spaces. Two examples are constructed to illustrate the corresponding results, respectively.

##### MSC:
 54H25 Fixed-point and coincidence theorems (topological aspects) 54A40 Fuzzy topology 54E40 Special maps on metric spaces
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##### References:
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