A Note on Brondsted's Fixed Point Theorem

TL;DR

This paper demonstrates that in uniformly convex Banach spaces, the conditions required for Brondsted's fixed point theorem can be weakened, broadening its applicability.

Contribution

It introduces relaxed conditions for Brondsted's fixed point theorem specifically in uniformly convex Banach spaces.

Findings

Conditions of the theorem can be relaxed in uniformly convex Banach spaces

Broader applicability of fixed point results in convex analysis

Potential for new fixed point theorems under weaker assumptions

Abstract

We show that for the case of uniformly convex Banach spaces the conditions of the Brondsted fixed point theorem can be relaxed.