On quantitative metastability for accretive operators

TL;DR

This paper extends previous results on metastability rates for approximate curves in Banach spaces to include resolvents of accretive operators, broadening the scope of convergence analysis in nonlinear functional analysis.

Contribution

It generalizes earlier metastability results to Reich's original convergence involving resolvents of accretive operators, enhancing understanding of their convergence behavior.

Findings

Metastability rates are established for resolvents of accretive operators.

The results extend previous convergence analyses to a broader class of operators.

The work confirms the applicability of metastability concepts to more general operator settings.

Abstract

Kohlenbach and the author have extracted a rate of metastability for approximate curves associated to continuous pseudocontractive self-mappings in Banach spaces which are uniformly convex and uniformly smooth, whose convergence is due to Reich. In this note, we show that this result may be extended to Reich's original convergence statement involving resolvents of accretive operators.