Applied Mathematics and Mechanics (English Edition) ›› 2014, Vol. 35 ›› Issue (7): 925-934.doi: https://doi.org/10.1007/s10483-014-1832-9

• 论文 • 上一篇    

Behavior of solution set for bilevel generalized mixed equilibrium problems in topological vector spaces

丁协平   

  1. College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610066, P. R. China
  • 收稿日期:2013-05-27 修回日期:2013-09-22 出版日期:2014-07-01 发布日期:2014-07-01
  • 通讯作者: Xie-ping DING, Professor, E-mail:xiepingding@hotmail.com E-mail:xiepingding@hotmail.com
  • 基金资助:
    Project supported by the Scientific Research Fund of Sichuan Normal University (No. 11ZDL01) and the Sichuan Province Leading Academic Discipline Project (No. SZD0406)

Behavior of solution set for bilevel generalized mixed equilibrium problems in topological vector spaces

Xie-ping DING   

  1. College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610066, P. R. China
  • Received:2013-05-27 Revised:2013-09-22 Online:2014-07-01 Published:2014-07-01
  • Supported by:
    Project supported by the Scientific Research Fund of Sichuan Normal University (No. 11ZDL01) and the Sichuan Province Leading Academic Discipline Project (No. SZD0406)

摘要: A new bilevel generalized mixed equilibrium problem (BGMEP) is introduced and studied in topological vector spaces. By using a minimax inequality, the existence of solutions and the behavior of solution set for the BGMEP are studied under quite mild conditions. These results are new and generalize some recent results in this field.

关键词: generalized mixed equilibrium problem (GMEP), bilevel generalized mixed equilibrium problem (BGMEP), monotonicity, minimax inequality, topological vector space

Abstract: A new bilevel generalized mixed equilibrium problem (BGMEP) is introduced and studied in topological vector spaces. By using a minimax inequality, the existence of solutions and the behavior of solution set for the BGMEP are studied under quite mild conditions. These results are new and generalize some recent results in this field.

Key words: generalized mixed equilibrium problem (GMEP), bilevel generalized mixed equilibrium problem (BGMEP), monotonicity, minimax inequality, topological vector space

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