%0 Journal Article
%T Stochastic Approximation Method for Fixed Point Problems
%A Ya. I. Alber
%A C. E. Chidume
%A Jinlu Li
%J Applied Mathematics
%P 2123-2132
%@ 2152-7393
%D 2012
%I Scientific Research Publishing
%R 10.4236/am.2012.312A293
%X <span>We study iterative processes of stochastic approximation for finding fixed points of weakly contractive and nonexpansive operators in Hilbert spaces under the condition that operators are given with random errors. We prove mean square convergence and convergence almost sure (a.s.) of iterative approximations and establish both asymptotic and nonasymptotic estimates of the convergence rate in degenerate and non-degenerate cases. Previously the stochastic approximation algorithms were studied mainly for optimization problems.</span> 
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%K Hilbert Spaces
%K Stochastic Approximation Algorithm
%K Weakly Contractive Operators
%K Nonexpansive Operators
%K Fixed Points
%K Convergence in Mean Square
%K Convergence Almost Sure (a.s.)
%K Nonasymptotic Estimates of Convergence Rate
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=26062