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