Operations Research Transactions ›› 2025, Vol. 29 ›› Issue (2): 201-213.doi: 10.15960/j.cnki.issn.1007-6093.2025.02.016

• Research Article • Previous Articles     Next Articles

An approximation theorem and generic convergence for generalized weakly-mixed vector quasi-equilibrium problem

Xudong FENG1, Wensheng JIA1,2,*()   

  1. 1. School of Mathematics and Statistics, Guizhou University, Guiyang 550025, Guizhou, China
    2. Guizhou Provincal Key Laboratory of Game, Decision and Control System, Guiyang 550025, Guizhou, China
  • Received:2020-07-04 Online:2025-06-15 Published:2025-06-12
  • Contact: Wensheng JIA E-mail:wsjia@gzu.edu.cn

Abstract:

The purpose of this paper is to study an approximation theorem and generic convergence of the generalized weakly-mixed vector quasi-equilibrium problem. Firstly, we give an existence theorem for the solution of generalized weakly-mixed vector quasi-equilibrium problems by using the Fan-Knaster-Kuratowski-Mazurkiewicz (Fan-KKM) lemma. Then, based on Simon's bounded rationality theory, we give an approximation theorem for generalized weakly-mixed vector quasi-equilibrium problems in a very general case. Finally, by using Fort's theorem, we obtain a generic convergence result for the solution of generalized weakly-mixed vector quasi-equilibrium problems in the sense of Baire classification.

Key words: generalized weakly-mixed vector quasi-equilibrium problem, Fan-KKM lemma, approximation theorem, generic convergence

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