Extensions of Edelstein's Theorem on Contractive Mappings

Abstract

The aim of this article is to provide extensions of Edelstein's theorem for a class of contractive mappings, namely cyclic contractive mappings. We prove the existence and convergence of best proximity points of a cyclic contractive map. We also discuss continuity properties of cyclic contractive maps. Finally, we give a characterization of such maps in the setting of a Hilbert space.