Rates of (T-)asymptotic regularity of the generalized Krasnoselskii-Mann-type iteration

TL;DR

This paper employs proof mining techniques to determine explicit convergence rates for a generalized iterative process related to nonexpansive mappings in uniformly convex spaces, including quadratic rates for specific parameters.

Contribution

It introduces a method to compute explicit rates of asymptotic regularity for generalized Krasnoselskii-Mann iterations, enhancing understanding of their convergence behavior.

Findings

Quadratic convergence rates for specific parameter choices

Explicit bounds on asymptotic regularity

Application of proof mining to iterative algorithms

Abstract

In this paper we use proof mining methods to compute rates of ($T$-)asymptotic regularity of the generalized Krasnoselskii-Mann-type iteration associated to a nonexpansive mapping $T:X\to X$ in a uniformly convex normed space $X$. For special choices of the parameter sequences, we obtain quadratic rates.