Bilevel equilibrium problems with lower and upper bounds in locally convex Hausdorff topological vector spaces

被引：8

作者：

Nguyen Van Hung ^{[1
,2
]}

O'Regan, Donal ^{[3
]}

机构：

[1] Ton Duc Thang Univ, Dept Management Sci & Technol Dev, Ho Chi Minh City, Vietnam

[2] Ton Duc Thang Univ, Fac Math & Stat, Ho Chi Minh City, Vietnam

[3] Natl Univ Ireland, Sch Math Stat & Appl Math, Galway, Ireland

来源：

TOPOLOGY AND ITS APPLICATIONS | 2020年 / 269卷

关键词：

Kakutani-Fan-Glicksberg fixed-point theorem; Equilibrium problems with lower and upper bounds; Bilevel equilibrium problems with lower and upper bounds; Existence conditions; Generic stability;

D O I：

10.1016/j.topol.2019.106939

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we introduce a new class of bilevel equilibrium problems with lower and upper bounds in locally convex Hausdorff topological vector spaces and establish some conditions for the existence of solutions to these problems using the Kakutani-Fan-Glicksberg fixed-point theorem. Then, we establish generic stability of set-valued mappings and we show the set of essential points of a map is a dense residual subset of a (Hausdorff) metric space of set-valued maps for bilevel equilibrium problems with lower and upper bounds. The results presented in the paper are new and extend the main results given by some authors in the literature. (C) 2019 Elsevier B.V. All rights reserved.

引用

页数：13

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