Best Proximity Point Results for MK-Proximal Contractions

Abstract

Let $A$ and $B$ be nonempty subsets of a metric space with the distance function d, and $T:A\to B$ is a given non-self-mapping. The purpose of this paper is to solve the nonlinear programming problem that consists in minimizing the real-valued function $x\mapsto d(x,Tx)$, where $T$ belongs to a new class of contractive mappings. We provide also an iterative algorithm to find a solution of such optimization problems.