Effective results on compositions of nonexpansive mappings

TL;DR

This paper establishes uniform bounds on the asymptotic regularity of iterative processes involving nonexpansive mappings within a broad class of geodesic spaces, extending previous results to more general settings.

Contribution

It provides the first uniform bounds on asymptotic regularity for nonexpansive mappings in $(r,\, ext{delta})$-convex spaces, generalizing known results beyond Hilbert spaces.

Findings

Uniform bounds on asymptotic regularity established

Results apply to a broad class of geodesic spaces

Extends previous work to $(r,\, ext{delta})$-convex spaces

Abstract

This paper provides uniform bounds on the asymptotic regularity for iterations associated to a finite family of nonexpansive mappings. We obtain our quantitative results in the setting of $(r,\delta)$-convex spaces, a class of geodesic spaces which generalizes metric spaces with a convex geodesic bicombing.