A rate of asymptotic regularity for the Mann iteration of $\kappa$-strict pseudo-contractions

TL;DR

This paper uses proof mining techniques to derive a uniform effective rate of asymptotic regularity for Mann iterations involving -strict pseudo-contractions in Hilbert spaces, enhancing understanding of convergence behavior.

Contribution

It provides the first explicit uniform rate of asymptotic regularity for Mann iterations with -strict pseudo-contractions using proof mining methods.

Findings

Established a uniform effective rate of asymptotic regularity

Applied proof mining to derive explicit convergence rates

Enhanced theoretical understanding of Mann iteration convergence

Abstract

In this paper we apply methods of proof mining to obtain a uniform effective rate of asymptotic regularity for the Mann iteration associated to $\kappa$-strict pseudo-contractions on convex subsets of Hilbert spaces.