Abstract
In this paper, we introduce a new concept of dominating proximal generalized Geraghty for two mappings and prove the existence and uniqueness of a common best proximity coincidence point in complete metric spaces. And also, we give an example for the main theorems. The main theorem is a generalization and improvement of some well-known theorems.
Highlights
The best proximity point problems have been attracted to many researchers as there are various applications in realworld problems
Let ðA, BÞ be a pair of nonempty subsets of a complete metric space ðX, dÞ, and let S, T : A ⟶ B be mappings
We give an idea of dominating proximal generalized Geraghty for a pair of mappings and give the existence and uniqueness theorem for a common best proximity coincidence point of these pairs in a complete metric space with some extra assumptions
Summary
The best proximity point problems have been attracted to many researchers as there are various applications in realworld problems. Most works focus on suggesting suitable conditions to promise the existence of approximate optimal solutions These results give the best proximity point theorem in a variety of approaches. The work of Geraghty [24] is one of several important results inspired by the Banach contraction principle for the existence of fixed points for self mappings in metric spaces. This result generalizes previous concepts by introducing the class Θ of all mappings θ : 1⁄20,∞Þ ⟶ 1⁄20, 1Þ such that nl→im∞θðtnÞ = 1 ⟹ nl→im∞tn = 0: ð1Þ. We investigate the existence and uniqueness of common best proximity coincidence points for any pairs of two mappings that are dominating proximal generalized Geraghty on a complete metric space. We consider some further results following from our main theorem
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