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Zbl 1171.90521
Long, Xian-Jun; Huang, Nan-Jing; Teo, Kok-Lay
Existence and stability of solutions for generalized strong vector quasi-equilibrium problem. (English)
[J] Math. Comput. Modelling 47, No. 3-4, 445-451 (2008). ISSN 0895-7177

Summary: We study the generalized strong vector quasi-equilibrium problem without assuming that the dual of the ordering cone has a weak$^{*}$ compact base. We establish an existence theorem of solutions for the generalized strong vector quasi-equilibrium problem by using Kakutani-Fan-Glicksberg fixed point theorem and discuss the closedness of the strong solution set. Moreover, we also derive a stability result for this problem.

MSC 2000:: *90C29 Multi-objective programming, etc.
90C47 Minimax problems

Keywords: vector quasi-equilibrium problem; set-valued mapping; existence of solutions; stability; Kakutani-Fan-Glicksberg fixed point theorem

Cited in: Zbl 1215.49010

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