Characterizations of strictly convex spaces and proximal uniform normal structure

TL;DR

This paper offers new characterizations of strictly convex Banach spaces and enhances a recent theorem related to cyclic uniform Lipschitzian mappings and proximal uniform normal structure.

Contribution

It introduces novel characterizations of strictly convex Banach spaces and improves upon a recent theorem in the context of cyclic mappings and normal structure.

Findings

New characterizations of strictly convex Banach spaces

Improved main theorem on cyclic uniform Lipschitzian mappings

Enhanced understanding of proximal uniform normal structure

Abstract

We provide a few characterizations of a strictly convex Banach space. Using this we improve the main theorem of [Digar, Abhik; Kosuru, G. Sankara Raju; Cyclic uniform Lipschitzian mappings and proximal uniform normal structure. Ann. Funct. Anal. 13 (2022)].