On the rate of convergence of Krasnosel’skiĭ-Mann iterations and their connection with sums of Bernoullis

R. Cominetti, J. A. Soto, J. Vaisman

Research output: Contribution to journalArticlepeer-review

29 Scopus citations

Abstract

In this paper we establish an estimate for the rate of convergence of the Krasnosel’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.

Original languageEnglish
Pages (from-to)757-772
Number of pages16
JournalIsrael Journal of Mathematics
Volume199
Issue number2
DOIs
StatePublished - 1 Mar 2014

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