The super fixed point property for asymptotically nonexpansive mappings

TL;DR

This paper proves the equivalence of super fixed point properties for nonexpansive and asymptotically nonexpansive mappings, leading to new fixed point theorems in specific Banach spaces and for commuting families.

Contribution

It establishes the equivalence of super fixed point properties for different classes of mappings and extends fixed point results to broader Banach space classes and commuting families.

Findings

Equivalence of super fixed point properties for nonexpansive and asymptotically nonexpansive mappings

Fixed point theorems in uniformly nonsquare and noncreasy Banach spaces

Generalization to commuting families of mappings

Abstract

We show that the super fixed point property for nonexpansive mappings and for asymptotically nonexpansive mappings in the intermediate sense are equivalent. As a consequence, we obtain fixed point theorems for asymptotically nonexpansive mappings in uniformly nonsquare and uniformly noncreasy Banach spaces. The results are generalized for commuting families of asymptotically nonexpansive mappings.