AN EXTRAGRADIENT METHOD FOR RELAXED COCOERCIVE VARIATIONAL INEQUALITY AND EQUILIBRIUM PROBLEMS

作     者：C.Jaiboon P.Kumam U.W.Humphries 

作者机构：King Mongkut's University of Technology ThonburiThailand 

出 版 物：《Analysis in Theory and Applications》 (分析理论与应用（英文刊）)

年 卷 期：2009年第25卷第4期

页      面：381-400页

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：Supported by King Mongkut's University of Technology Thonburi.KMUTT,(CSEC Project No.E01008) supported by the Faculty of Applied Liberal Arts RMUTR Research Fund and King Mongkut's Diamond scholarship for fostering special academic skills by KMUTT 

主　　题：nonexpansive mapping relaxed cocoercive mapping variational inequality,fixed point equilibrium problem extragradient method 

摘      要：The purpose of this paper is to investigate the problem of finding the common element of the set of common fixed points of a countable family of nonexpansive mappings, the set of an equilibrium problem and the set of solutions of the variational inequality prob- lem for a relaxed cocoercive and Lipschitz continuous mapping in Hilbert spaces. Then, we show that the sequence converges strongly to a common element of the above three sets under some parameter controlling conditions, which are connected with Yao, Liou, Yao[17], Takahashi[12] and many others.