an:06319492
Zbl 1429.54058
Shen, Yonghong; Chen, Wei
Fixed point theorems for cyclic contraction mappings in fuzzy metric spaces
EN
Fixed Point Theory Appl. 2013, Paper No. 133, 9 p. (2013).
00328752
2013
j
54H25 54A40 54E40
Edelstein contraction theorem; cyclic contraction; fuzzy metric space
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 \textit{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 \textit{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.
Zbl 0664.54032; Zbl 1333.54050