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
收藏
页数：21
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