Existence of vector mixed variational inequalities in Banach spaces

被引：8

作者：

Ceng, L. C. ^{[2
]}

Cubiotti, R. ^{[3
]}

Yao, J. C. ^{[1
]}

机构：

[1] Natl Sun Yat Sen Univ, Dept Appl Math, Kaohsiung 804, Taiwan

[2] Shanghai Normal Univ, Dept Math, Shanghai 200234, Peoples R China

[3] Univ Messina, Dept Math, I-98166 Messina, Italy

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2009年 / 70卷 / 03期

基金：

美国国家科学基金会;

关键词：

Vector mixed variational inequality; Ky Fan's lemma; Hausdorff metric; Brouwer's fixed point theorem; Composite monotonicity; Compositely complete semicontinuity; EQUILIBRIUM PROBLEMS; MINIMAL ELEMENT;

D O I：

10.1016/j.na.2008.01.039

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The purpose of this paper is to study the solvability for vector mixed variational inequalities (for short, VMVI) in Banach spaces. Utilizing Ky Fan's Lemma and Nadler's theorem, we derive the solvability for VMVIs with compositely monotone vector multifunctions. On the other hand, we first introduce the concepts of compositely complete semicontinuity and compositely strong semicontinuity for vector multifunctions. Then we prove the solvability for VMVIs without monotonicity assumption by using these concepts and by applying Brouwer's fixed point theorem. The results presented in this paper are extensions and improvements of some earlier and recent results in the literature. (C) 2008 Elsevier Ltd. All rights reserved.

引用

页码：1239 / 1256

页数：18

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