Acta mathematica scientia,Series B ›› 2010, Vol. 30 ›› Issue (4): 1257-1268.doi: 10.1016/S0252-9602(10)60122-1

• Articles • Previous Articles     Next Articles

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)

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

CLC Number: 

  • 91B50
Trendmd