Quantitative results on a generalized viscosity approximation method

TL;DR

This paper investigates the asymptotic behavior of a generalized viscosity approximation method in nonlinear settings, providing quantitative convergence results using proof mining techniques in hyperbolic and CAT(0) spaces.

Contribution

It introduces new quantitative analysis of a generalized viscosity approximation method in nonlinear spaces, extending previous qualitative results.

Findings

Quantitative rates of asymptotic regularity in W-hyperbolic spaces

Rates of metastability in CAT(0) spaces

Application of proof mining to nonlinear approximation methods

Abstract

In this paper, we study, in a nonlinear setting, the asymptotic behaviour of a generalized viscosity approximation method associated with a countable family of nonexpansive mappings satisfying resolvent-like conditions. We apply proof mining methods to obtain quantitative results on asymptotic regularity in W-hyperbolic spaces and rates of metastability in CAT(0) spaces.