Best proximity point theorems for generalized JSC- proximal contractions

Abstract

This article presents best proximity point theorems for new classes of non-self mappings, known as generalized JSC-proximal contractions in metric spaces.Presented results and theorems are generalizations of [8] and [9] Mathematical Subject Classification:41A65; 46B20; 47H10.Let A and B be the non-empty subsets of a metric space. We know that the following notations and notions are used in the sequel. d(A, B) = inf{d(x, y) : x ∈ A and y ∈ B} A 0 = {x ∈ A : d(x, y) = d(A, B) for some y ∈ B} B 0 = {y ∈ B : d(x, y) = d(A, B) for some x ∈ A} If A and B are closed subsets of a normed linear space such that d(A, B) > 0, then A 0 and B 0 are contained in the boundaries of A and B respectively [7].Definition 2.1. [9] The Set B is said to be approximately compact with respect to A if every sequence {y n } of B satisfying the condition that d(x, y n ) → 3 Main Results Definition 3.1. A mapping T : A → B is said to be generalized JSCproximal contraction of the first kind if there exists ψ ∈ Ψ and non-negative numbers q, r, s, t with q + r + s + 2t < 1 such that the conditions d(u 1 , T x 1 ) = d(A, B) and d(u 2 , T x 2 ) = d(A, B)