Fixed point theorems for cyclic contraction mappings in fuzzy metric spaces

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 Grabiec. Additionally, we extend a fixed point theorem in G-complete fuzzy metric spaces given by Shen et al. to M-complete fuzzy metric spaces. Meantime, two examples are constructed to illustrate the corresponding results, respectively.