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

Abstract

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