Semicontinuity of the solution multifunctions of the parametric generalized operator equilibrium problems

被引：10

作者：

Kim, Won Kyu ^{[1
]}

Kum, Sangho ^{[1
]}

Lee, Kyoung Hee ^{[2
]}

机构：

[1] Chungbuk Natl Univ, Dept Math Educ, Cheongju 361763, South Korea

[2] Korea Univ Technol & Educ, Div Liberal Arts, Chunan 330708, South Korea

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2009年 / 71卷 / 12期

关键词：

Parametric generalized operator equilibrium and quasi-equilibrium; problem; Upper and lower semicontinuity; QUASI-VARIATIONAL INEQUALITIES; EXISTENCE; MAPS; SET;

D O I：

10.1016/j.na.2009.04.036

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we first introduce the parametric form of the generalized operator equilibrium problem and generalized operator quasi-equilibrium problem due to Kum and Kim [S. Kum, W. K. Kim, On generalized operator quasi-equilibrium problems, J. Math. Anal. Appl. 345 (2008) 559-565]. Next, we consider the upper and lower semicontinuity properties for the parametric generalized operator equilibrium problem (simply, PGOEP) and the parametric generalized operator quasi-equilibrium problem (simply, PGOQEP). Our semicontinuity properties of the solution sets for (PGOEP) and (PGOQEP) can be suitable for the stability properties of many kinds of nonlinear problems, e. g., the operator equilibrium problem, operator quasi-equilibrium problem, operator variational-like inequality problem, operator variational inequality problem, operator minimization problem and vector equilibrium problem. (C) 2009 Elsevier Ltd. All rights reserved.

引用

页码：E2182 / E2187

页数：6

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