Title: Rates of convergence for inexact Krasnosel'skii-Mann iterations in Banach spaces,
Abstract: We study the convergence of an inexact version of the classical
Krasnosel'skii-Mann iteration for computing fixed points of nonexpansive maps.
Our main result establishes a new metric bound for the fixed-point residuals,
from which we derive their rate of convergence as well as the convergence of
the iterates towards a fixed point. The results are applied to three variants
of the basic iteration: infeasible iterations with approximate projections, the
Ishikawa iteration, and diagonal Krasnosels'kii-Mann schemes. The results are
also extended to continuous time in order to study the asymptotics of
nonautonomous evolution equations governed by nonexpansive operators.