Modified Block Iterative Method for Solving Convex Feasibility Problem, Equilibrium Problems and Variational Inequality Problems

The purpose of this paper is by using the modified block iterative method to propose an algorithm for finding a common element in the intersection of the set of common fixed points of an infinite family of quasi-C-asymptotically nonexpansive and the set of solutions to an equilibrium problem and the...

Full description

Saved in:
Bibliographic Details
Published in:Acta mathematica Sinica. English series Vol. 28; no. 4; pp. 741 - 758
Main Authors: Zhang, Shi Sheng, Chan, Chi Kin, Joseph Lee, H. W.
Format: Journal Article
Language:English
Published: Heidelberg Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 01.04.2012
Springer Nature B.V
Subjects:
Algorithms
Applied mathematics
Asymptotic methods
Banach space
Banach spaces
Banach空间
Blocking
Convergence
Equilibrium
Feasibility
Hilbert space
Inequalities
Iterative methods
Mathematical analysis
Mathematics
Mathematics and Statistics
Studies
Theorems
不动点集
修改
变分不等式问题
平衡问题
强收敛定理
极大单调映象
迭代求解
Modified block iterative algorithm
47H09
nonexpansive mapping
47J05
quasi
asymptotically nonexpansive mapping
relatively nonexpansive mapping
generalized projection
49J25
ISSN:1439-8516, 1439-7617
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:The purpose of this paper is by using the modified block iterative method to propose an algorithm for finding a common element in the intersection of the set of common fixed points of an infinite family of quasi-C-asymptotically nonexpansive and the set of solutions to an equilibrium problem and the set of solutions to a variational inequality. Under suitable conditions some strong convergence theorems are established in 2-uniformly convex and uniformly smooth Banach spaces. As applications we utilize the results presented in the paper to solving the convex feasibility problem （CFP） and zero point problem of maximal monotone mappings in Banach spaces. The results presented in the paper improve and extend the corresponding results announced by many authors.
Bibliography:The purpose of this paper is by using the modified block iterative method to propose an algorithm for finding a common element in the intersection of the set of common fixed points of an infinite family of quasi-C-asymptotically nonexpansive and the set of solutions to an equilibrium problem and the set of solutions to a variational inequality. Under suitable conditions some strong convergence theorems are established in 2-uniformly convex and uniformly smooth Banach spaces. As applications we utilize the results presented in the paper to solving the convex feasibility problem （CFP） and zero point problem of maximal monotone mappings in Banach spaces. The results presented in the paper improve and extend the corresponding results announced by many authors.
11-2039/O1
Modified block iterative algorithm, quasi-φ-asymptotically nonexpansive mapping, quasi-φ-nonexpansive mapping, relatively nonexpansive mapping, generalized projection
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ObjectType-Article-1
ObjectType-Feature-2
content type line 23
ISSN:1439-8516
1439-7617
DOI:10.1007/s10114-011-0099-3