Asymptotically nonexpansive mappings in uniformly convex hyperbolic spaces

TL;DR

This paper establishes a fixed point theorem for asymptotically nonexpansive mappings in uniformly convex hyperbolic spaces and introduces effective iteration results using logical methods.

Contribution

It provides new fixed point results and effective iteration techniques for asymptotically nonexpansive mappings in hyperbolic spaces, advancing fixed point theory.

Findings

Fixed point theorem for asymptotically nonexpansive mappings

Effective results on Krasnoselski-Mann iterations

Application of logic methods to fixed point proofs

Abstract

This paper provides a fixed point theorem for asymptotically nonexpansive mappings in uniformly convex hyperbolic spaces as well as new effective results on the Krasnoselski-Mann iterations of such mappings. The latter were found using methods from logic and the paper continues a case study in the general program of extracting effective data from prima-facie ineffective proofs in the fixed point theory of such mappings.