Yong-hong Shen - School of Mathematics and Statistics, Tianshui Normal Univer- sity, Tianshui ۷۴۱۰۰۱, People's Republic of China
Dong Qiu - College of Mathematics and Physics, Chongqing University of Posts and Telecommunications, Chongqing ۴۰۰۰۶۵, People's Republic of China
Wei Chen - School of Information, Capital University of Economics and Business, Beijing, ۱۰۰۰۷۰, People's Republic of China

In this paper, the notion of cyclic \varphi-contraction in fuzzymetric spaces is introduced and a fixed point theorem for this typeof mapping is established. Meantime, an example is provided toillustrate this theorem. The main result shows that a self-mappingon a G-complete fuzzy metric space has a unique fixed point if itsatisfies the cyclic \varphi-contraction. Afterwards, some results inconnection with the fixed point are given.

Cyclic representation, Cyclic varphi-contraction, Fixed point, G-Cauchy sequence, G-complete fuzzy metric space