Auxiliary Principle and Algorithm of Solutions for a New System of Generalized Mixed Equilibrium Problems in Banach Spaces

作     者：Ding, X. P. 

作者机构：Sichuan Normal Univ Coll Math & Software Sci Chengdu 610068 Sichuan Peoples R China 

出 版 物：《JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS》 (优选法理论与应用杂志)

年 卷 期：2012年第155卷第3期

页      面：796-809页

核心收录：

学科分类：1201[管理学-管理科学与工程(可授管理学、工学学位)] 07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：Scientific Research Fun of Sichuan Normal University [11ZDL01] Sichuan Province Leading Academic Discipline Project [SZD0406] 

主　　题：System of generalized mixed equilibrium problems Auxiliary principle Iterative algorithm Banach space 

摘      要：In this paper, we study a new system of generalized mixed equilibrium problems involving nonmonotone set-valued mappings and nondifferential bifunctions in Banach spaces. First, a system of auxiliary generalized mixed equilibrium problems are introduced. By using a minimax inequality, the existence and uniqueness of solutions of the system of auxiliary generalized mixed equilibrium problems is proved. Next, by using the auxiliary principle technique, an iterative algorithm for solving the system of generalized mixed equilibrium problems is constructed. Finally, the existence of solutions and the convergence of iterative sequences generated by the algorithm are proved under suitable conditions. These results improve, unify, and generalize many corresponding known results given in literature.