On proximal uniform normal structure and relatively nonexpansive mappings

TL;DR

This paper offers an alternative proof for a key result involving proximal normal structure and relatively nonexpansive mappings, characterizes strictly convex spaces, and discusses conditions for proximal sub-pairs in Banach spaces.

Contribution

It introduces an alternative approach using proximal uniform normal structure and provides new characterizations and conditions related to Banach space geometry.

Findings

Provides an alternative proof of a central result from prior work.

Characterizes strictly convex spaces via new conditions.

Establishes sufficient conditions for proximal sub-pairs in Banach spaces.

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