Fixed point theory for cyclic \(\varphi\)-contractions in fuzzy metric spaces. (English) Zbl 1333.54050

Shen, Yong-Hong; Qiu, Dong; Chen, Wei

Iran. J. Fuzzy Syst. 10, No. 4, 125-133 (2013).

Summary: In this paper, the notion of cyclic \(\varphi\)-contraction in fuzzy metric spaces is introduced and a fixed point theorem for this type of mapping is established. Meantime, an example is provided to illustrate this theorem. The main result shows that a self-mapping on a G-complete fuzzy metric space has a unique fixed point if it satisfies the cyclic \(\varphi\)-contraction. Afterwards, some results inconnection with the fixed point are given.

MSC:

54H25	Fixed-point and coincidence theorems (topological aspects)
54A40	Fuzzy topology

Keywords:

cyclic representation; cyclic \(\varphi\)-contraction; fixed point; G-Cauchy sequence; G-complete fuzzy metric space