@article{c3036d6251964342b50febb40f41226e,
title = "On the rate of convergence of Krasnosel{\textquoteright}skiĭ-Mann iterations and their connection with sums of Bernoullis",
abstract = "In this paper we establish an estimate for the rate of convergence of the Krasnosel{\textquoteright}skiĭ-Mann iteration for computing fixed points of non-expansive maps. Our main result settles the Baillon-Bruck conjecture [3] on the asymptotic regularity of this iteration. The proof proceeds by establishing a connection between these iterates and a stochastic process involving sums of non-homogeneous Bernoulli trials. We also exploit a new Hoeffdingtype inequality to majorize the expected value of a convex function of these sums using Poisson distributions.",
author = "R. Cominetti and Soto, {J. A.} and J. Vaisman",
note = "Funding Information: ∗ Supported by Fondecyt 1100046 and N{\'u}cleo Milenio Informaci{\'o}n y Coordinaci{\'o}n en Redes ICM/FIC P10-024F. ∗∗Supported by Basal-Conicyt project and N{\'u}cleo Milenio Informaci{\'o}n y Coordi-naci{\'o}n en Redes ICM/FIC P10-024F. Received July 6, 2012 and in revised form November 27, 2012 Publisher Copyright: {\textcopyright} 2014, Hebrew University Magnes Press.",
year = "2014",
month = mar,
day = "1",
doi = "10.1007/s11856-013-0045-4",
language = "English",
volume = "199",
pages = "757--772",
journal = "Israel Journal of Mathematics",
issn = "0021-2172",
publisher = "Springer New York",
number = "2",
}