New systems of generalized vector quasi-equilibrium problems in product FC-spaces

Authors:
Xie Ping Ding
Affiliations:
College of Mathematics and Software Science, Sichuan Normal University, Chengdu, People's Republic of China 610066
Venue:
Journal of Global Optimization
Year:
2010

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Abstract

The notions of C i (x)-FC-diagonally quasiconvex, C i (x)-FC-quasiconvex and C i (x)-FC-quasiconvex-like for set-valued mappings are introduced in FC-spaces without convexity structure. By applying these notions and a maximal element theorem for a family of set-valued mappings on product FC-space due to author, some new existence theorems of solutions for four new classes of systems of generalized vector quasi-equilibrium problems are proved in noncompact FC-spaces. These results improve and generalize some recent known results in literature to noncompact FC-spaces.