具变动控制结构的对称广义强向量拟均衡问题及其应用

doi:10.12341/jssms13908

系统科学与数学 ›› 2020, Vol. 40 ›› Issue (6): 1037-1049.DOI: 10.12341/jssms13908

具变动控制结构的对称广义强向量拟均衡问题及其应用

黄文君¹，王三华^1,2，张宇新¹

1. 南昌大学数学系, 南昌 330031;2. 南昌大学管理科学与工程博士后流动站, 南昌 330031

出版日期:2020-06-25 发布日期:2020-08-25

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黄文君，王三华，张宇新. 具变动控制结构的对称广义强向量拟均衡问题及其应用[J]. 系统科学与数学, 2020, 40(6): 1037-1049.

HUANG Wenjun, WANG Sanhua, ZHANG Yuxin. Symmetric Generalized Strong Vector Quasi-Equilibrium Problem with Variable Ordering Structures with Applications[J]. Journal of Systems Science and Mathematical Sciences, 2020, 40(6): 1037-1049.

Symmetric Generalized Strong Vector Quasi-Equilibrium Problem with Variable Ordering Structures with Applications

HUANG Wenjun¹,WANG Sanhua ^1,2 ,ZHANG Yuxin ¹

1. Department of Mathematics, Nanchang University, Nanchang 330031; 2. Post-Doctor Station of Management Science and Engineering, Nanchang University, Nanchang 330031

Online:2020-06-25 Published:2020-08-25

讨论了具变动控制结构的对称广义强向量拟均衡问题. 在锥值映射具无限上连续性条件下, 利用Fan-KKM定理和Kakutani-Fan-Glicksberg不动点定理, 建立了解的存在性结果, 进一步, 还得出了其解集的紧性结论. 作为应用, 文中还给出了广义强向量拟鞍点问题解的存在性及其解集的紧性结果. 这些结果推广和发展了近期已有文献的相关结论.

关键词： 对称广义强向量拟均衡问题, 鞍点问题, 变动控制结构, 解的存在性, 无限上连续.

In this paper, a symmetric generalized strong vector quasi-equilibrium problem with variable ordering structures is introduced and discussed. Under the condition of cosmically upper continuity for the cone-valued mapping, some existence theorems are obtained by using the Fan-KKM theorem and the Kakutani-Fan-Glicksberg fixed point theorem. Moreover, the conclusions of compactness of the solution set for this problem are also derived. As an application, some theorems of existence of solutions and compactness of solution set are obtained for generalized strong vector quasi-saddle point problem. These results extend and develop some corresponding ones existing in the recent literatures.

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