Rates of asymptotic regularity for the alternating Halpern-Mann iteration

Laurentiu Leustean; Pedro Pinto

paper

Rates of asymptotic regularity for the alternating Halpern-Mann iteration

arXiv:2206.02226

Abstract

In this paper we extend to $U C W$ -hyperbolic spaces the quantitative asymptotic regularity results for the alternating Halpern-Mann iteration obtained by Dinis and the second author for CAT(0) spaces. These results are new even for uniformly convex normed spaces. Furthermore, for a particular choice of the parameter sequences, we compute linear rates of asymptotic regularity in $W$ -hyperbolic spaces and quadratic rates of $T$ - and $U$ -asymptotic regularity in CAT(0) spaces.