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

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.