Strong convergence for the modified Mann's iteration of λ-strict pseudocontraction

被引：2

作者：

Song, Yisheng ^{[1
,2
]}

Wang, Hongjun ^{[1
]}

机构：

[1] Henan Normal Univ, Coll Math & Informat Sci, Xinxiang 453007, Henan, Peoples R China

[2] Hong Kong Polytech Univ, Dept Appl Math, Kowloon, Hong Kong, Peoples R China

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2014年 / 237卷

关键词：

lambda-Strict pseudocontraction; Modified Mann's iteration; 2-Uniformly smooth Banach space; PSEUDO-CONTRACTIONS; THEOREMS; ALGORITHMS; MAPPINGS;

D O I：

10.1016/j.amc.2014.03.097

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, for an lambda-strict pseudocontraction T, we prove strong convergence of the modified Mann's iteration defined by x(n+1) = beta(n)u + gamma(n)x(n) + (1 - beta(n) - gamma(n)) [alpha(n)Tx(n) + (1 - alpha(n))x(n)] where {alpha(n)}, {beta(n)} and {gamma(n)} in (0, 1) satisfy: ( i) 0 <= alpha(n) <= lambda/k(2) with lim inf(n ->infinity)alpha(n)(lambda - K-2 alpha(n)) > 0 ( ii) lim(n ->infinity)beta(n) = 0 and Sigma(infinity)(n-1)beta(n) = infinity; ( iii) lim sup(n ->infinity)gamma(n) < 1. Our results unify and improve some existing results. (C) 2014 Elsevier Inc. All rights reserved.

引用

页码：405 / 410

页数：6

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