On the Suzuki nonexpansive-type mappings

TL;DR

This paper proves fixed point existence for certain nonexpansive-type mappings in specific Banach spaces, extending known results to uniformly nonsquare and nearly uniformly noncreasy spaces.

Contribution

It establishes fixed point theorems for mappings satisfying conditions (C) or (C_λ) in Banach spaces with M(X)>1, including uniformly nonsquare and nearly uniformly noncreasy spaces.

Findings

Fixed points exist for mappings satisfying (C) or (C_λ) in specified Banach spaces.

Results extend fixed point theory to uniformly nonsquare Banach spaces.

Theorems also apply to nearly uniformly noncreasy spaces.

Abstract

It is shown that if $C$ is a nonempty convex and weakly compact subset of a Banach space $X$ with $M(X)>1$ and $T:C\rightarrow C$ satisfies condition $(C)$ or is continuous and satisfies condition $(C_{\lambda})$ for some $\lambda \in (0,1)$, then $T$ has a fixed point. In particular, our theorem holds for uniformly nonsquare Banach spaces. A similar statement is proved for nearly uniformly noncreasy spaces.