Abstract
In this paper, we introduce fuzzy multiplicative metric space and prove some best proximity point theorems for single-valued and multivalued proximal contractions on the newly introduced space. As corollaries of our results, we prove some fixed-point theorems. Also, we present best proximity point theorems for Feng-Liu-type multivalued proximal contraction in fuzzy metric space. Moreover, we illustrate our results with some interesting examples.
Highlights
Introduction and PreliminariesBest proximity point is the generalization of fixed point and is useful when contraction map is not a self-map that is T : A ⟶ B where A ∩ B = φ
They proved a fixed-point theorem for newly defined multivalued contraction which is stated as follows: “Let ðM, dÞ be a complete metric space, T : M ⟶ CðMÞ, where Cð
We prove a best proximity theorem for Feng-Liutype multivalued contraction in fuzzy multiplicative metric space
Summary
Fan [1] presented best approximation theorem which is stated as follows: “If K is a nonempty compact convex subset of a Hausdorff locally convex topological vector space E and T : K ⟶ E is a continuous non-self-mapping, there exists an element μ in K such a way that dðμ, TμÞ = dðTμ, KÞ.”. Another way of defining multivalued contraction is approached by Feng and Liu [9] They proved a fixed-point theorem for newly defined multivalued contraction which is stated as follows: “Let ðM , dÞ be a complete metric space, T : M ⟶ CðMÞ, where Cð. Vetro and Salimi [20] proved best proximity point theorem in fuzzy metric spaces. We obtain some best proximity point theorems for Feng-Liutype multivalued non-self-maps on fuzzy multiplicative metric space
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