Acta mathematica scientia, Series B >
MATHEMATICAL PROGRAMS WITH SYSTEM OF GENERALIZED VECTOR QUASI-EQUILIBRIUM CONSTRAINTS IN FC-SPACES
Received date: 2007-11-27
Revised date: 2009-09-28
Online 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)
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.
DING Xie-Ping . MATHEMATICAL PROGRAMS WITH SYSTEM OF GENERALIZED VECTOR QUASI-EQUILIBRIUM CONSTRAINTS IN FC-SPACES[J]. Acta mathematica scientia, Series B, 2010 , 30(4) : 1257 -1268 . DOI: 10.1016/S0252-9602(10)60122-1
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