Quantitative asymptotic regularity results for the composition of two mappings

TL;DR

This paper applies proof mining techniques to derive explicit rates of asymptotic regularity and metastability for sequences generated by composing two firmly nonexpansive mappings.

Contribution

It introduces a novel approach using proof mining to obtain quantitative convergence rates for compositions of nonexpansive mappings.

Findings

Derived explicit rates of asymptotic regularity

Established metastability bounds for the sequences

Applied proof mining techniques to nonexpansive mappings

Abstract

In this paper, we use techniques which originate from proof mining to give rates of asymptotic regularity and metastability for a sequence associated to the composition of two firmly nonexpansive mappings.