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2012 Strong Convergence Theorems for Nonexpansive Semigroups and Variational Inequalities in Banach Spaces
Haiqing Wang, Yongfu Su, Hong Zhang
J. Appl. Math. 2012(SI03): 1-19 (2012). DOI: 10.1155/2012/641479

Abstract

Let X be a uniformly convex Banach space and S = { T ( s ) : 0 s < } be a nonexpansive semigroup such that F ( S ) = s > 0 F ( T ( s ) ) . Consider the iterative method that generates the sequence { x n } by the algorithm x n + 1 = α n f ( x n ) + β n x n + ( 1 - α n - β n ) ( 1 / s n ) 0 s n T ( s ) x n d s , n 0 , where { α n } , { β n } , and { s n } are three sequences satisfying certain conditions, f : C C is a contraction mapping. Strong convergence of the algorithm { x n } is proved assuming X either has a weakly continuous duality map or has a uniformly Gâteaux differentiable norm.

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Haiqing Wang. Yongfu Su. Hong Zhang. "Strong Convergence Theorems for Nonexpansive Semigroups and Variational Inequalities in Banach Spaces." J. Appl. Math. 2012 (SI03) 1 - 19, 2012. https://doi.org/10.1155/2012/641479

Information

Published: 2012
First available in Project Euclid: 3 January 2013

zbMATH: 1235.49028
MathSciNet: MR2889103
Digital Object Identifier: 10.1155/2012/641479

Rights: Copyright © 2012 Hindawi

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Vol.2012 • No. SI03 • 2012
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