# Rates of convergence for iterative solutions of equations involving set-valued accretive operators

## TL;DR

This paper derives explicit convergence rates for iterative methods solving equations with set-valued accretive operators, revealing a common underlying pattern in existing proofs using a logic-based approach.

## Contribution

It introduces a modular proof mining method to extract explicit convergence rates and unifies various convergence proofs under a common framework.

## Key findings

- Explicit convergence rates depending on uniform accretivity modulus
- Identification of a common pattern in diverse convergence proofs
- Application of proof mining to set-valued accretive operator equations

## Abstract

This paper studies proofs of strong convergence of various iterative algorithms for computing the unique zeros of set-valued accretive operators that also satisfy some weak form of uniform accretivity at zero. More precisely, we extract explicit rates of convergence from these proofs which depend on a modulus of uniform accretivity at zero, a concept first introduced by A. Koutsoukou-Argyraki and the first author in 2015. Our highly modular approach, which is inspired by the logic-based proof mining paradigm, also establishes that a number of seemingly unrelated convergence proofs in the literature are actually instances of a common pattern.