Common Best Proximity Coincidence Point Theorem for Dominating Proximal Generalized Geraghty in Complete Metric Spaces

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.

Common best proximity points of some graph-theoretical notions of dominating pairs

“…Later, Chen [7] created a class of pairs of mapping (P, Q) where Q is proximally dominated by P, and obtained some common best proximity point results. The results were then discovered by introducing a type of Geraghty contractions in [21].…”

“…In this article, we consider a metric space (X, d) which is endowed with graph G. Motivated by the work in [21], we provide a class of pairs of mappings in X associated with auxiliary functions introduced in [17]. Then, some sufficient conditions for the existence and uniqueness of a common best proximity point in X are presented.…”

Common Best Proximity Point Theorems for Generalized Dominating with Graphs and Applications in Differential Equations

“…As a consequence, this definition established the existence and uniqueness outcomes for the best proximity points in the case of closed subsets of complete metric spaces. Recently, in [21], A. Khemphet et al generated the idea of dominating proximal generalized Geraghty for pairs of functions by employing the class F above and proved the existence and uniqueness theorems for common best proximity points in complete metric spaces. This work extended previous results in the literature and, in particular, extended recent results by L. Chen; see [22].…”

Common Best Proximity Point Theorems in JS-Metric Spaces Endowed with Graphs

“…Hussain and his coauthors are amongst those who have actively contributed results to this research area (see [11,12], where different kinds of contractions are employed; see [13,14], where generalized notions of metric spaces are considered; and see [15] for best proximity results in nonlinear dynamical systems). There are many more results on common best proximity points in the literature (see [16][17][18][19][20] for some of the key works).…”