Construction of fixed points of asymptotically nonexpansive mappings in uniformly convex hyperbolic spaces

TL;DR

This paper extends fixed point theory to uniformly convex hyperbolic spaces by constructing convergent sequences for asymptotically nonexpansive mappings, building on prior existence results.

Contribution

It adapts Moloney's construction to produce strongly convergent sequences to fixed points in uniformly convex hyperbolic spaces.

Findings

Established strong convergence of sequences to fixed points

Extended fixed point results to a broader class of spaces

Provided a constructive method for fixed point approximation

Abstract

Kohlenbach and Leustean have shown in 2010 that any asymptotically nonexpansive self-mapping of a bounded nonempty $UCW$-hyperbolic space has a fixed point. In this paper, we adapt a construction due to Moloney in order to provide a sequence that converges strongly to such a fixed point.