Fixed point theory for cyclic $\varphi$-contractions in fuzzy metric spaces

Document Type: Research Paper

Authors

1 School of Mathematics and Statistics, Tianshui Normal Univer- sity, Tianshui 741001, People's Republic of China

2 College of Mathematics and Physics, Chongqing University of Posts and Telecommunications, Chongqing 400065, People's Republic of China

3 School of Information, Capital University of Economics and Business, Beijing, 100070, People's Republic of China

Abstract

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 in
connection with the fixed point are given.

Keywords


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