Ordered non-Archimedean fuzzy metric spaces and some fixed point results.(English)Zbl 1191.54033

In this paper, the authors introduce the concept of fuzzy order $$\psi$$-contractive mappings and prove two fixed point theorems on ordered non-Archimedean fuzzy metric spaces for fuzzy order $$\psi$$-contractive type mappings. The authors also prove a common fixed point theorem for weakly increasing single-valued mappings in a complete fuzzy metric space endowed with a partial order induced by an appropriate function. They discuss Kirk’s problem on an extension of Caristi’s theorem.

MSC:

 54H25 Fixed-point and coincidence theorems (topological aspects) 54A40 Fuzzy topology
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References:

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