Convergence theorems for fixed point problems and variational inequality problems in Hilbert spaces

被引：11
|
作者：
Yao, Yonghong [1 ]
Liou, Yeong-Cheng [2 ]
Chen, Rudong [1 ]
机构：
[1] Tianjin Polytech Univ, Dept Math, Tianjin 300160, Peoples R China
[2] Cheng Shiu Univ, Dept Informat Management, Kaohsiung 833, Taiwan
来源：
MATHEMATISCHE NACHRICHTEN | 2009年 / 282卷 / 12期
关键词：
Fixed point; monotone mapping; variational inequality; strong convergence; Hilbert space; NONEXPANSIVE-MAPPINGS; MONOTONE-OPERATORS;
D O I：
10.1002/mana.200610817
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we introduce an iterative scheme for finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inequality for an alpha-inverse strongly monotone mapping in a Hilbert space. We show that the sequence converges strongly to a common element of two sets under some mild conditions on parameters. (C) 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
引用
收藏
页码：1827 / 1835
页数：9
相关论文
共 50 条
  • [1] CONVERGENCE THEOREMS FOR FIXED POINT PROBLEMS AND VARIATIONAL INEQUALITY PROBLEMS
    Yao, Yonghong
    Liou, Yeong-Cheng
    Chen, Rudong
    [J]. JOURNAL OF NONLINEAR AND CONVEX ANALYSIS, 2008, 9 (02) : 239 - 248
  • [2] Strong Convergence Theorems for Variational Inequality Problems and Fixed Point Problems in Banach Spaces
    Cai, Gang
    Bu, Shangquan
    [J]. BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, 2013, 36 (02) : 525 - 540
  • [3] 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
    [J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2013, 247 : 34 - 52
  • [4] WEAK CONVERGENCE THEOREMS FOR GENERAL EQUILIBRIUM PROBLEMS AND VARIATIONAL INEQUALITY PROBLEMS AND FIXED POINT PROBLEMS IN BANACH SPACES
    Cai, Gang
    Bu, Shangquan
    [J]. ACTA MATHEMATICA SCIENTIA, 2013, 33 (01) : 303 - 320
  • [5] WEAK CONVERGENCE THEOREMS FOR GENERAL EQUILIBRIUM PROBLEMS AND VARIATIONAL INEQUALITY PROBLEMS AND FIXED POINT PROBLEMS IN BANACH SPACES
    蔡钢
    步尚金
    [J]. Acta Mathematica Scientia, 2013, 33 (01) : 303 - 320
  • [6] Strong convergence of a general iterative method for variational inequality problems and fixed point problems in Hilbert spaces
    Qin, Xiaolong
    Shang, Meijuan
    Zhou, Haiyun
    [J]. APPLIED MATHEMATICS AND COMPUTATION, 2008, 200 (01) : 242 - 253
  • [7] Strong convergence theorems for split variational inequality problems in Hilbert spaces
    Sun, Wenlong
    Lu, Gang
    Jin, Yuanfeng
    Peng, Zufeng
    [J]. AIMS MATHEMATICS, 2023, 8 (11): : 27291 - 27308
  • [8] Strong convergence theorems for fixed point problems, variational inequality problems, and equilibrium problems
    Yao, Zhangsong
    Liou, Yeong-Cheng
    Zhu, Li-Jun
    Lo, Ching-Hua
    Wu, Chen-Chang
    [J]. JOURNAL OF INEQUALITIES AND APPLICATIONS, 2015,
  • [9] Strong convergence theorems for fixed point problems, variational inequality problems, and equilibrium problems
    Zhangsong Yao
    Yeong-Cheng Liou
    Li-Jun Zhu
    Ching-Hua Lo
    Chen-Chang Wu
    [J]. Journal of Inequalities and Applications, 2015
  • [10] Convergence Theorems on an Iterative Method for Variational Inequality Problems and Fixed Point Problems
    Qin, Xiaolong
    Kang, Shin Min
    [J]. BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, 2010, 33 (01) : 155 - 167
12345