广义弱混合向量拟平衡问题的逼近定理和通有收敛性

doi:10.15960/j.cnki.issn.1007-6093.2025.02.016

运筹学学报（中英文） ›› 2025, Vol. 29 ›› Issue (2): 201-213.doi: 10.15960/j.cnki.issn.1007-6093.2025.02.016

广义弱混合向量拟平衡问题的逼近定理和通有收敛性

冯旭东¹, 贾文生¹^,²^,*()

1. 贵州大学数学与统计学院, 贵州贵阳 550025
2. 贵州省博弈、决策与控制系统重点实验室, 贵州贵阳 550025

收稿日期:2020-07-04 出版日期:2025-06-15 发布日期:2025-06-12
通讯作者: 贾文生 E-mail:wsjia@gzu.edu.cn
基金资助:
国家自然科学基金(12061020);国家自然科学基金(71961003);贵州省自然科学基金(20201Y284);贵州省自然科学基金(20205016);贵州省自然科学基金(2021088);贵州省自然科学基金(20215640)

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

Xudong FENG¹, Wensheng JIA¹^,²^,*()

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

摘要/Abstract

摘要：

本文研究广义弱混合向量拟平衡问题的逼近定理和通有收敛性。首先利用Fan-Knaster-Kuratowski-Mazurkiewicz (Fan-KKM) 引理给出了广义弱混合向量拟平衡问题解的存在性定理。然后基于Simon的有限理性理论, 在较弱的条件下给出了广义弱混合向量拟平衡问题的一个逼近定理。最后运用Fort定理, 证明了在Baire分类意义下广义弱混合向量拟平衡问题的解具有通有收敛的结果。

关键词: 广义弱混合向量拟平衡问题, Fan-KKM引理, 逼近定理, 通有收敛

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

中图分类号:

O225

冯旭东, 贾文生. 广义弱混合向量拟平衡问题的逼近定理和通有收敛性[J]. 运筹学学报（中英文）, 2025, 29(2): 201-213.

Xudong FENG, Wensheng JIA. An approximation theorem and generic convergence for generalized weakly-mixed vector quasi-equilibrium problem[J]. Operations Research Transactions, 2025, 29(2): 201-213.

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广义弱混合向量拟平衡问题的逼近定理和通有收敛性

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

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