A Coincidence Best Proximity Point Problem inG-Metric Spaces

Abstract

The aim of this paper is to initiate the study of coincidence best proximity point problem in the setup of generalized metric spaces. Some results dealing with existence and uniqueness of a coincidence best proximity point of mappings satisfying certain contractive conditions in such spaces are obtained. An example is provided to support the result proved herein. Our results generalize, extend, and unify various results in the existing literature.

Best proximity point results for Suzuki-Edelstein proximal contractions via auxiliary functions

“…If we take φ(t) = kt, k ∈ [0, 1), in Theorem 3.5 we have the following: Corollary 3.6. Suppose that A and B are two non empty closed subsets of a complete metric space (X, d) with A 0 φ, a function δ : [0, 1) → (0, 1 2 ] and for all x, y ∈ A a mapping T : A → B be such that…”

Best Proximity Point Results for Generalized Θ-Contractions and Application to Matrix Equations

“…Thus, a best proximity pair theorem furnishes sufficient conditions for the existence of an optimal approximate solution x, known as a best proximity point of the mapping F, satisfying the condition that d(x, Fx) = d(A, B). Many authors established the existence and convergence of fixed and best proximity points under certain contractive conditions in different metric spaces (see e.g., [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30] and references therein).…”

Best proximity coincidence point theorems for generalized non-linear contraction mappings

“…These points are known as best proximity points and were introduced by [12] and modified by Sadiq Basha in [13]. Best proximity point theorems for several types of non-self mappings have been derived in [13][14][15][16][17][18][19][20][21]. Recently, Geraghty [6] obtained a generalization of the Banach contraction principle in the setting of complete metric spaces by considering an auxiliary function.…”