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Fixed points in weak non-Archimedean fuzzy metric spaces. (English) Zbl 1206.54066
Summary: D. Miheţ [Fuzzy Sets Syst. 159, No. 6, 739–744 (2008); erratum ibid. 161, No. 8, 1150–1151 (2010; Zbl 1171.54330)] proved a theorem which assures the existence of a fixed point for fuzzy \(\psi \)-contractive mappings in the framework of complete non-Archimedean fuzzy metric spaces. Motivated by this, we introduce a notion of weak non-Archimedean fuzzy metric space and prove that the weak non-Archimedean fuzzy metric induces a Hausdorff topology. We utilize this new notion to obtain some common fixed point results for a pair of generalized contractive type mappings.

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