Best proximity point theorems for reckoning optimal approximate solutions

Abstract

Abstract Given a non-self mapping from A to B, where A and B are subsets of a metric space, in order to compute an optimal approximate solution of the equation S x = x , a best proximity point theorem probes into the global minimization of the error function x ⟶ d ( x , S x ) corresponding to approximate solutions of the equation S x = x . This paper presents a best proximity point theorem for generalized contractions, thereby furnishing optimal approximate solutions, called best proximity points, to some non-linear equations. Also, an iterative algorithm is presented to compute such optimal approximate solutions. MSC:90C26, 90C30, 41A65, 46B20, 47H10, 54H25.