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
收藏
页码：1816 / 1828
页数：13
相关论文
共 50 条
  • [41] Hybrid extragradient method for generalized mixed equilibrium problems and fixed point problems in Hilbert space
    Li, Suhong
    Li, Lihua
    Cao, Lijun
    He, Xiujuan
    Yue, Xiaoyun
    FIXED POINT THEORY AND APPLICATIONS, 2013,
  • [42] Hybrid extragradient method for generalized mixed equilibrium problems and fixed point problems in Hilbert space
    Suhong Li
    Lihua Li
    Lijun Cao
    Xiujuan He
    Xiaoyun Yue
    Fixed Point Theory and Applications, 2013
  • [43] Strong convergence theorems for variational inequality, equilibrium and fixed point problems with applications
    Shenghua Wang
    Giuseppe Marino
    Yeong-Cheng Liou
    Journal of Global Optimization, 2012, 54 : 155 - 171
  • [44] The subgradient extragradient method for solving mixed equilibrium problems and fixed point problems in hilbert spaces
    Farid, Mohammad
    Journal of Applied and Numerical Optimization, 2019, 1 (03): : 335 - 345
  • [45] A hybrid extragradient method extended to fixed point problems and equilibrium problems
    Pham Ngoc Anh
    OPTIMIZATION, 2013, 62 (02) : 271 - 283
  • [46] A Hybrid Extragradient Method for Pseudomonotone Equilibrium Problems and Fixed Point Problems
    Pham Ngoc Anh
    BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, 2013, 36 (01) : 107 - 116
  • [47] WEAK CONVERGENCE OF A HYBRID ITERATIVE SCHEME WITH ERRORS FOR EQUILIBRIUM PROBLEMS AND COMMON FIXED POINT PROBLEMS
    Kim, Seung-Hyun
    Lee, Byung-Soo
    JOURNAL OF THE KOREAN SOCIETY OF MATHEMATICAL EDUCATION SERIES B-PURE AND APPLIED MATHEMATICS, 2014, 21 (03): : 195 - 206
  • [48] On strong convergence of an iterative algorithm for common fixed point and generalized equilibrium problems
    Jian-Min Song
    Journal of Inequalities and Applications, 2014
  • [49] An iterative method for equilibrium problems and fixed point problems
    Min, Chen
    Jiang, Qiaohong
    APPLIED SCIENCE, MATERIALS SCIENCE AND INFORMATION TECHNOLOGIES IN INDUSTRY, 2014, 513-517 : 382 - 385
  • [50] On strong convergence of an iterative algorithm for common fixed point and generalized equilibrium problems
    Song, Jian-Min
    JOURNAL OF INEQUALITIES AND APPLICATIONS, 2014,
12345