Existence and stability of solutions of a global setvalued optimization problem

Abstract

In this paper we consider a best proximity point problem whose purpose is to determine the minimum distance between two sets. It is a global optimization problem by its very nature which is solved by converting it into a problem of finding an optimal approximate solution of a fixed point inclusion for a coupled setvalued mapping. Two solutions are obtained simultaneously through an iteration. We introduce certain definitions which are used in our theorems. We investigate the data dependence property of the proximity point sets and establish a weak stability result for the proximity point sets. There are some illustrative examples. The broad area of the present study is setvalued optimization.

Keywords

• metric space
• coupled best proximity point
• proximal α-dominating mapping
• generalized coupled proximal contraction
• data dependence property
• stability