  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 non-empty proximal sub-pair for a pair in a
Banach space are discussed.
