On the rate of convergence of krasnosel’skII–mann iterations and their connection with sums of Bernoullis
Author
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Cominetti Cotti-Cometti, Roberto
es_CL
Author
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Soto Andrade, Jorge
Author
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Vaisman Romero, José Antonio
es_CL
Admission date
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2014-12-15T20:35:07Z
Available date
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2014-12-15T20:35:07Z
Publication date
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2014
Cita de ítem
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Israel Journal of Mathematics 199 (2014), 757–772
en_US
Identifier
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DOI: 10.1007/s11856-013-0045-4
Identifier
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https://repositorio.uchile.cl/handle/2250/126620
General note
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Artículo de publicación ISI
en_US
Abstract
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In this paper we establish an estimate for the rate of convergence of the
Krasnosel’skiˇı–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.
en_US
Patrocinador
dc.description.sponsorship
Supported by Fondecyt 1100046 and N´ucleo Milenio Informaci´on y Coordinaci´on
en Redes ICM/FIC P10-024F.
Supported by Basal-Conicyt project and N´ucleo Milenio Informaci´on y Coordinaci
´on en Redes ICM/FIC P10-024F.