BEST PROXIMITY POINT THEOREM FOR MAPPINGS WITH A CONTRACTIVE ITERATE ON P SETS

There are many generalizations of the Banach contraction principle. In this paper we prove a result that combines three of them: best proximity points of a cyclic map in a complete metric space with the UC property, the contraction condition holding for a subset of all elements, and the mapping being with a contractive iterate at a point. We illustrate this result by proving Eldred and Veermani’s classic theorem as a corollary to ours and illustrate an application of it by an example.