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arXiv · 1206.4195

On the rate of convergence of Krasnoselski-Mann iterations and their connection with sums of Bernoullis

Roberto Cominetti·José A. Soto·José Vaisman
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Abstract

In this paper we establish an estimate for the rate of convergence of the Krasnosel'ski\v{\i}-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 Hoeffding-type inequality to majorize the expected value of a convex function of these sums using Poisson distributions.

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Roberto Cominetti, José A. Soto, José Vaisman. 2012-06-19. On the rate of convergence of Krasnoselski-Mann iterations and their connection with sums of Bernoullis. https://doi.org/10.1007/s11856-013-0045-4

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