Iterative algorithm for solutions to new system of generalized mixed implicit equilibrium  

作　　者：丁协平 

机构地区：[1]College of Mathematics and Software Science,Sichuan Normal University

出　　处：《Applied Mathematics and Mechanics(English Edition)》2013年第1期113-126,共14页应用数学和力学（英文版）

基　　金：Project supported by the Sichuan Province Leading Academic Discipline Project(No.SZD0406);the Scientific Research Fund of Sichuan Normal University(No.11ZDL01)

摘　　要：A new system of generalized mixed implicit equilibrium problems （SGMIEP） involving nonmonotone set-valued mappings is introduced and studied in real reflexive Banach spaces. First, an auxiliary mixed equilibrium problem （AMEP） is introduced. The existence and the uniqueness of the solutions to the AMEP are proved under quite mild assumptions without any coercive conditions. Next, by using the solution mapping of the AMEP, a system of generalized equation problems （SGEP） is considered, and its equivalence with the SGMIEP is shown. By using the SGEP, a new iterative algorithm for solving the SGMIEP is proposed and analyzed. The strong convergence of the iterative sequences generated by the algorithm is proved under suitable conditions. These results are new, which unify and generalize some recent results in this field.A new system of generalized mixed implicit equilibrium problems （SGMIEP） involving nonmonotone set-valued mappings is introduced and studied in real reflexive Banach spaces. First, an auxiliary mixed equilibrium problem （AMEP） is introduced. The existence and the uniqueness of the solutions to the AMEP are proved under quite mild assumptions without any coercive conditions. Next, by using the solution mapping of the AMEP, a system of generalized equation problems （SGEP） is considered, and its equivalence with the SGMIEP is shown. By using the SGEP, a new iterative algorithm for solving the SGMIEP is proposed and analyzed. The strong convergence of the iterative sequences generated by the algorithm is proved under suitable conditions. These results are new, which unify and generalize some recent results in this field.

关 键 词：system of generalized mixed implicit equilibrium problems （SGMIEP） auxiliary mixed equilibrium problem （AMEP） system of generalized equation problems（SGEP） iterative algorithm reflexive Banach space 

分 类 号：O177.2[理学—数学] O241.6[理学—基础数学]