Abstract
The introduction of the common limit range property on V -fuzzy metric spaces is the foremost aim of this paper. Furthermore, significant results for coupled maps are proven by employing this property on V -fuzzy metric spaces. More precisely, we introduce the notion of C L R Ω -property for the mappings Θ : M × M → M and Ω : M → M . We utilize our new notion to present and prove our new fixed point results.
Highlights
Introduction and PreliminariesMustafa and Sims [1] brought the though of the notion of G-metric spaces as a generalization of metric spaces
Several influential mathematicians considered the notion of fuzzy sets to introduce many exciting notions in the field of mathematics, such as fuzzy differential equations, fuzzy logic and fuzzy metric spaces
In 1975, Kramosil and Michalek [5] employed the notion of fuzzy sets to introduce the notion of fuzzy metric spaces
Summary
Introduction and PreliminariesMustafa and Sims [1] brought the though of the notion of G-metric spaces as a generalization of metric spaces. The mappings Θ : M × M → M and Ω : M → M are said to compatible on V -fuzzy metric spaces if limr→+∞ V (ΩΘ( β r , ηr ), ΩΘ( β r , ηr ), · · ·, ΩΘ( β r , ηr ), Θ(Ωβ r , Ωηr ), t) = 1 and limr→+∞ V (ΩΘ(ηr , β r ), ΩΘ(ηr , β r ), · · ·, ΩΘ(ηr , β r ), Θ(Ωηr , Ωβ r ), t) = 1, whenever { β r } and {ηr } are sequences in M such that limr→+∞ Ω( β r ) = limr→+∞ Θ( β r , ηr ) = β and limr→+∞ Ω(ηr ) = limr→+∞ Θ(ηr , β r ) = η for all β, η ∈ M, t > 0.
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