Strong convergence of implicit viscosity approximation methods for pseudocontractive mappings in Banach spaces

被引：5

作者：

Ceng, Lu-Chuan ^{[2
,3
]}

Petrusel, Adrian ^{[4
]}

Wong, Mu-Ming ^{[1
]}

Yu, Su-Jane ^{[5
]}

机构：

[1] Chung Yuan Christian Univ, Dept Appl Math, Chungli 32023, Taiwan

[2] Shanghai Normal Univ, Dept Math, Shanghai 200234, Peoples R China

[3] Sci Comp Key Lab Shanghai Univ, Shanghai, Peoples R China

[4] Univ Babes Bolyai, Dept Appl Math, Cluj Napoca 400084, Romania

[5] Natl Hsinchu Univ Educ, Dept Appl Math, Hsinchu 30014, Taiwan

来源：

OPTIMIZATION | 2011年 / 60卷 / 06期

基金：

美国国家科学基金会;

关键词：

strong convergence; implicit viscosity approximation method; pseudocontractive mapping; contraction mapping; nonexpansive mapping; fixed point; variational inequality; uniformly smooth Banach space; MIXED EQUILIBRIUM PROBLEMS; FIXED-POINTS; PERTURBED MAPPINGS; MANN ITERATION; EQUATIONS; THEOREMS;

D O I：

10.1080/02331931003622547

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

Let C be a nonempty closed convex subset of a uniformly smooth Banach space X. Let f : C -> C be a fixed contraction mapping, S : C -> C be a nonexpansive mapping and T : C -> C be a pseudocontractive mapping. Let {alpha(n)}, {beta(n)} and {gamma(n)} be three real sequences in (0, 1) such that alpha(n) + beta(n) + gamma(n) <= 1. For arbitrary x(0) is an element of C, the sequence {x(n)} is generated by x(n) = (1 - alpha(n) - beta(n) - gamma(n))x(n-1) + alpha(n)f(x(n-1)) + beta(n)Sx(n-1) + gamma(n)Tx(n) for all n >= 1. It is proven that under some conditions, {x(n)} converges strongly to a fixed point of T, which solves some variational inequality.

引用

页码：659 / 670

页数：12

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