Best proximity point theorems: resolution of an important non-linear programming problem

Abstract

The purpose of this article is to resolve the non-linear programming problem of globally minimizing the real valued function \({x \longrightarrow d(x, Sx)}\) where S is a non-self-mapping in the setting of a metric space with the distance function ‘d’. An iterative algorithm is also furnished to find a solution of such global optimization problems. As a consequence, one can determine an optimal approximate solution to some equations of the form Sx = x.