Strong convergence theorems of iterative scheme based on the extragradient method for mixed equilibrium problems and fixed point problems

被引：72

作者：

Peng, Jian-Wen ^{[2
]}

Yao, Jen-Chih ^{[1
]}

机构：

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

[2] Chongqing Normal Univ, Coll Math & Comp Sci, Chongqing 400047, Peoples R China

来源：

MATHEMATICAL AND COMPUTER MODELLING | 2009年 / 49卷 / 9-10期

基金：

芬兰科学院; 中国国家自然科学基金;

关键词：

Mixed equilibrium problem; Extragradient method; Nonexpansive mapping; Monotone mapping; Variational inequality; Strong convergence; Fixed point; VARIATIONAL INEQUALITY PROBLEMS; NONEXPANSIVE-MAPPINGS; MONOTONE MAPPINGS; ALGORITHMS; OPERATORS; OPTIMIZATION; SPACES; WEAK;

D O I：

10.1016/j.mcm.2008.11.014

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

In this paper, a new iterative scheme based on the extragradient method for finding a common element of the set of solutions of a mixed equilibrium problem, the set of fixed points of a family of finitely nonexpansive mappings and the set of solutions of the variational inequality for a monotone, Lipschitz continuous mapping is proposed. A strong convergence theorem for this iterative scheme in Hilbert spaces is established. Applications to optimization problems are given. (C) 2009 Elsevier Ltd. All rights reserved.

引用

页码：1816 / 1828

页数：13

共 50 条

[31] Strong and weak convergence theorems for general mixed equilibrium problems and variational inequality problems and fixed point problems in Hilbert spaces
Cai, Gang
Bu, Shangquan
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2013, 247 : 34 - 52
[32] STRONG CONVERGENCE OF AN ITERATIVE METHOD FOR VARIATIONAL INEQUALITY PROBLEMS AND FIXED POINT PROBLEMS
Qin, Xiaolong
Kang, Shin Min
Su, Yongfu
Shang, Meijuan
ARCHIVUM MATHEMATICUM, 2009, 45 (02): : 147 - 158
[33] Existence and Convergence Theorems for Equilibrium Problems and Fixed Point Problems
Haddadi, Mohammad Reza
Dehghanian, Mehdi
SOUTHEAST ASIAN BULLETIN OF MATHEMATICS, 2018, 42 (04) : 559 - 568
[34] Iterative Methods of Weak and Strong Convergence Theorems for the Split Common Solution of the Feasibility Problems, Generalized Equilibrium Problems, and Fixed Point Problems
Rezapour, Shahram
Wang, Yuanheng
Zakeri, Seyyed Hasan
JOURNAL OF MATHEMATICS, 2020, 2020
[35] Strong Convergence Theorems of Common Elements for Equilibrium Problems and Fixed Point Problems in Banach Spaces
Xing-hui GAO 1
Acta Mathematicae Applicatae Sinica, 2012, (02) : 337 - 350
[36] Strong Convergence Theorems of Common Elements for Equilibrium Problems and Fixed Point Problems in Banach Spaces
Xinghui GAO Haiyun ZHOU College of Mathematics and Computer ScienceYanan UniversityYanan China Department of MathematicsShijiazhuang Mechanical Engineering UniversityShijiazhuang China
Acta Mathematicae Applicatae Sinica(English Series), 2012, 28 (02) : 337 - 350
[37] Strong convergence theorems of common elements for equilibrium problems and fixed point problems in banach spaces
Xing-hui Gao
Hai-yun Zhou
Acta Mathematicae Applicatae Sinica, English Series, 2012, 28 : 337 - 350
[38] Strong Convergence Theorems of Common Elements for Equilibrium Problems and Fixed Point Problems in Banach Spaces
Gao, Xing-hui
Zhou, Hai-yun
ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES, 2012, 28 (02): : 337 - 350
[39] This Strong and weak convergence theorems for split equilibrium problems and fixed point problems in Banach spaces
Guo, Baohua
Ping, Ping
Zhao, Haiqing
Cho, Yeol Je
JOURNAL OF NONLINEAR SCIENCES AND APPLICATIONS, 2017, 10 (06): : 2886 - 2901
[40] Strong convergence theorems for variational inequality, equilibrium and fixed point problems with applications
Wang, Shenghua
Marino, Giuseppe
Liou, Yeong-Cheng
JOURNAL OF GLOBAL OPTIMIZATION, 2012, 54 (01) : 155 - 171

← 1 2 3 4 5 →