A global optimality result using nonself mappings

Abstract

In this paper we consider a classical global optimization problem of obtaining minimum distance between pairs of closed sets by using an extension of the weak contraction mapping. The extension is accomplished with the help of three control functions. P-property of pairs of closed sets has been used. The result has several corollaries and an illustrative example. One corollary extends an existing work on best proximity point problem. The example shows that the extension is actual.