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

doi:10.1007/s10483-013-1657-x

Applied Mathematics and Mechanics (English Edition) ›› 2013, Vol. 34 ›› Issue (1): 113-126.doi: https://doi.org/10.1007/s10483-013-1657-x

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

丁协平

College of Mathematics and Software Science, Sichuan Normal University,Chengdu 610066, P. R. China

收稿日期:2012-02-13 修回日期:2012-03-01 出版日期:2013-01-03 发布日期:2013-01-03
通讯作者: 丁协平 E-mail:xieping ding@hotmail.com
基金资助:
the Sichuan Province Leading Academic Discipline Project (No. SZD0406) and the Scientific Research Fund of Sichuan Normal University (No. 11ZDL01)

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

DING Xie-Ping

College of Mathematics and Software Science, Sichuan Normal University,Chengdu 610066, P. R. China

Received:2012-02-13 Revised:2012-03-01 Online:2013-01-03 Published:2013-01-03
Contact: Xie-ping DING E-mail:xieping ding@hotmail.com
Supported by:
the Sichuan Province Leading Academic Discipline Project (No. SZD0406) and the Scientific Research Fund of Sichuan Normal University (No. 11ZDL01)

摘要/Abstract

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.

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, nonlinear system, boundary value problem, diagonalization, singular perturbation

Abstract: 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.

Key words: system of generalized mixed implicit equilibrium problems (SGMIEP), auxiliary mixed equilibrium problem (AMEP), system of generalized equation problems (SGEP), iterative algorithm, reflexive Banach space, nonlinear system, boundary value problem, diagonalization, singular perturbation

丁协平. Iterative algorithm for solutions to new system of generalized mixed implicit equilibrium[J]. Applied Mathematics and Mechanics (English Edition), 2013, 34(1): 113-126.

DING Xie-Ping. Iterative algorithm for solutions to new system of generalized mixed implicit equilibrium[J]. Applied Mathematics and Mechanics (English Edition), 2013, 34(1): 113-126.

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

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

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