数学物理学报(英文版) ›› 2010, Vol. 30 ›› Issue (4): 1257-1268.doi: 10.1016/S0252-9602(10)60122-1

• 论文 • 上一篇    下一篇

MATHEMATICAL PROGRAMS WITH SYSTEM OF GENERALIZED VECTOR QUASI-EQUILIBRIUM CONSTRAINTS IN FC-SPACES

丁协平   

  1. College of Mathematics and Software Science, Sichuan Normal University Chengdu, Sichuan 610066, China
  • 收稿日期:2007-11-27 修回日期:2009-09-28 出版日期:2010-07-20 发布日期:2010-07-20
  • 基金资助:

    This project was supported by the Scientific Research Fun of Sichuan Normal University (09ZDL04) and the Sichuan Province Leading Academic Discipline Project (SZD0406)

MATHEMATICAL PROGRAMS WITH SYSTEM OF GENERALIZED VECTOR QUASI-EQUILIBRIUM CONSTRAINTS IN FC-SPACES

 DING Xie-Ping   

  1. College of Mathematics and Software Science, Sichuan Normal University Chengdu, Sichuan 610066, China
  • Received:2007-11-27 Revised:2009-09-28 Online:2010-07-20 Published:2010-07-20
  • Supported by:

    This project was supported by the Scientific Research Fun of Sichuan Normal University (09ZDL04) and the Sichuan Province Leading Academic Discipline Project (SZD0406)

PDF (PC)

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摘要：

In this article, four new classes of systems of generalized vector quasi-equilibrium problems are introduced and studied in FC-spaces without convexity structure. The notions of Ci(x)-FC-partially diagonally quasiconvex, Ci(x)-FC-quasiconvex, and Ci(x)-FC-quasiconvex-like for set-valued mappings are also introduced in FC-spaces. By applying these notions and a maximal element theorem, the nonemptyness and compactness of solution sets for four classes of systems of generalized vector quasi-equilibrium problems are proved in
noncompact FC-spaces. As applications, some new existence theorems of solutions for mathematical programs with system of generalized vector quasi-equilibrium constraints are obtained in FC-spaces. These results improve and generalize some recent known results in literature.

关键词: Maximal element, system of generalized vector quasi-equilibrium problems, Mathematical program, Ci(x)-FC-partially diagonally quasiconvex, Ci(x)-FC-quasiconvex, Ci(x)-FC-quasiconvex-like, FC-space

Abstract:

In this article, four new classes of systems of generalized vector quasi-equilibrium problems are introduced and studied in FC-spaces without convexity structure. The notions of Ci(x)-FC-partially diagonally quasiconvex, Ci(x)-FC-quasiconvex, and Ci(x)-FC-quasiconvex-like for set-valued mappings are also introduced in FC-spaces. By applying these notions and a maximal element theorem, the nonemptyness and compactness of solution sets for four classes of systems of generalized vector quasi-equilibrium problems are proved in
noncompact FC-spaces. As applications, some new existence theorems of solutions for mathematical programs with system of generalized vector quasi-equilibrium constraints are obtained in FC-spaces. These results improve and generalize some recent known results in literature.

Key words: Maximal element, system of generalized vector quasi-equilibrium problems, Mathematical program, Ci(x)-FC-partially diagonally quasiconvex, Ci(x)-FC-quasiconvex, Ci(x)-FC-quasiconvex-like, FC-space

中图分类号: 

  • 91B50
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