Strong and weak convergence theorems for an infinite family of nonexpansive mappings and applications

被引：5

作者：

Ceng, L. C. ^{[3
,4
]}

Wong, N. C. ^{[2
]}

Yao, J. C. ^{[1
]}

机构：

[1] Kaohsiung Med Univ, Ctr Gen Educ, Kaohsiung 807, Taiwan

[2] Natl Sun Yat Sen Univ, Dept Appl Math, Kaohsiung 804, Taiwan

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

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

来源：

FIXED POINT THEORY AND APPLICATIONS | 2012年

基金：

美国国家科学基金会;

关键词：

hybrid viscosity approximation method; nonexpansive mapping; strictly convex Banach space; uniformly smooth Banach space; reflexive Banach space with weakly continuous duality map; COMMON FIXED-POINTS; VISCOSITY APPROXIMATION METHODS; ITERATIVE METHOD; BANACH; PROJECTIONS; SEQUENCES; OPERATORS;

D O I：

10.1186/1687-1812-2012-117

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, let E be a reflexive and strictly convex Banach space which either is uniformly smooth or has a weakly continuous duality map. We consider the hybrid viscosity approximation method for finding a common fixed point of an infinite family of nonexpansive mappings in E. We prove the strong convergence of this method to a common fixed point of the infinite family of nonexpansive mappings, which solves a variational inequality on their common fixed point set. We also give a weak convergence theorem for the hybrid viscosity approximation method involving an infinite family of nonexpansive mappings in a Hilbert space. MSC: 47H17, 47H09, 47H10, 47H05.

引用

页数：21

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