数学物理学报(英文版) ›› 2013, Vol. 33 ›› Issue (1): 303-320.doi: 10.1016/S0252-9602(12)60212-4

• 论文 • 上一篇    

WEAK CONVERGENCE THEOREMS FOR GENERAL EQUILIBRIUM PROBLEMS AND VARIATIONAL INEQUALITY PROBLEMS AND FIXED POINT PROBLEMS IN BANACH SPACES

蔡钢|步尚全   

  1. Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China
  • 收稿日期:2010-10-11 修回日期:2011-10-10 出版日期:2013-01-20 发布日期:2013-01-20
  • 通讯作者: 步尚全,sbu@math.tsinghua.edu.cn E-mail:caigang-aaaa@163.com; sbu@math.tsinghua.edu.cn
  • 基金资助:

    This work was supported by the NSF of China (11171172).

WEAK CONVERGENCE THEOREMS FOR GENERAL EQUILIBRIUM PROBLEMS AND VARIATIONAL INEQUALITY PROBLEMS AND FIXED POINT PROBLEMS IN BANACH SPACES

 CAI Gang, BU Shang-Quan   

  1. Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China
  • Received:2010-10-11 Revised:2011-10-10 Online:2013-01-20 Published:2013-01-20
  • Contact: Shang-Quan,sbu@math.tsinghua.edu.cn E-mail:caigang-aaaa@163.com; sbu@math.tsinghua.edu.cn
  • Supported by:

    This work was supported by the NSF of China (11171172).

摘要:

In this paper, we introduce two new iterative algorithms for finding a common element of the set of solutions of a general equilibrium problem and the set of solutions of the variational inequality for an inverse-strongly monotone operator and the set of common fixed points of two infinite families of relatively nonexpansive mappings or the set of common fixed points of an infinite family of relatively quasi-nonexpansive mappings in Banach spaces. Then we study the weak convergence of the two iterative sequences. Our results improve and extend the results announced by many others.

关键词: weak convergence, relatively nonexpansive mapping, equilibrium problem, variational inequality

Abstract:

In this paper, we introduce two new iterative algorithms for finding a common element of the set of solutions of a general equilibrium problem and the set of solutions of the variational inequality for an inverse-strongly monotone operator and the set of common fixed points of two infinite families of relatively nonexpansive mappings or the set of common fixed points of an infinite family of relatively quasi-nonexpansive mappings in Banach spaces. Then we study the weak convergence of the two iterative sequences. Our results improve and extend the results announced by many others.

Key words: weak convergence, relatively nonexpansive mapping, equilibrium problem, variational inequality

中图分类号: 

  • 47H09