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