Diametrically Relatively Nonexpansive Mappings and a Characterization of Proximal Normal Structure

Abstract

We consider a new type of cyclic (noncyclic) mappings, called diametrically relatively nonexpansive maps which contains properly the class of cyclic (noncyclic) relatively nonexpansive mappings. For such mappings we obtain existence results of best proximity points (pairs) in the framework of Busemann convex spaces and generalize the recent conclusions in this direction. We also present a characterization of proximal normal structure in term of best proximity points (pairs) for diametrically relatively nonexpansive mappings.