@article{0360ffaa303c4f1e8fd2f7e57de6b523,
title = "Rates of convergence for inexact Krasnosel{\textquoteright}skii–Mann iterations in Banach spaces",
abstract = "We study the convergence of an inexact version of the classical Krasnosel{\textquoteright}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{\textquoteright}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.",
keywords = "Evolution equations, Fixed point iterations, Nonexpansive maps, Rates of convergence",
author = "Mario Bravo and Roberto Cominetti and Mat{\'i}as Pavez-Sign{\'e}",
note = "Funding Information: This work was partially supported by N{\'u}cleo Milenio Informaci{\'o}n y Coordinaci{\'o}n en Redes ICM/FIC RC130003. Mario Bravo was partially funded by FONDECYT 11151003. Roberto Cominetti and Mat{\'i}as Pavez-Sign{\'e} gratefully acknowledge the support provided by FONDECYT 1130564 and FONDECYT 1171501. Publisher Copyright: {\textcopyright} 2018, Springer-Verlag GmbH Germany, part of Springer Nature and Mathematical Optimization Society.",
year = "2019",
month = may,
day = "1",
doi = "10.1007/s10107-018-1240-1",
language = "English",
volume = "175",
pages = "241--262",
journal = "Mathematical Programming",
issn = "0025-5610",
publisher = "Springer-Verlag GmbH and Co. KG",
number = "1-2",
}