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Author (up) Bravo, M.; Cominetti, R. doi  openurl
  Title Sharp convergence rates for averaged nonexpansive maps Type Journal Article
  Year 2018 Publication Israel Journal Of Mathematics Abbreviated Journal Isr. J. Math.  
  Volume 227 Issue 1 Pages 163-188  
  Keywords  
  Abstract We establish sharp estimates for the convergence rate of the Kranosel'skiA-Mann fixed point iteration in general normed spaces, and we use them to show that the optimal constant of asymptotic regularity is exactly . To this end we consider a nested family of optimal transport problems that provide a recursive bound for the distance between the iterates. We show that these bounds are tight by building a nonexpansive map T: [0, 1](N) -> [0, 1](N) that attains them with equality, settling a conjecture by Baillon and Bruck. The recursive bounds are in turn reinterpreted as absorption probabilities for an underlying Markov chain which is used to establish the tightness of the constant 1/root pi.  
  Address [Bravo, Mario] Univ Santiago Chile, Dept Matemat & Ciencia Computac, Alameda Libertador Bernardo Ohiggins 3363, Santiago, Chile, Email: mario.bravo.g@usach.cl;  
  Corporate Author Thesis  
  Publisher Hebrew Univ Magnes Press Place of Publication Editor  
  Language English Summary Language Original Title  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 0021-2172 ISBN Medium  
  Area Expedition Conference  
  Notes WOS:000442512900006 Approved no  
  Call Number UAI @ eduardo.moreno @ Serial 909  
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