On proximal uniform normal structure and relatively nonexpansive mappings

Abstract

The main objective of this article is to provide an alternative approach to the central result of [Eldred, A. Anthony, Kirk, W. A., Veeramani, P., Proximal normal structure and relatively nonexpansive mappings, Studia Math., vol 171(3), ( 2005) 283-293] using proximal uniform normal structure. Also we provide characterizations of a strictly convex space. Finally, sufficient conditions for the existence of a nonempty proximal sub-pair for a pair in a Banach space are discussed.