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

作　　者：蔡钢 步尚金 

机构地区：[1]Department of Mathematical Sciences,Tsinghua University

出　　处：《Acta Mathematica Scientia》2013年第1期303-320,共18页数学物理学报（B辑英文版）

基　　金：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.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 

分 类 号：O177.91[理学—数学]