Existence theorems for generalized vector variational inequalities with a variable ordering relation

被引：20

作者：

Ceng, Lu-Chuan ^{[1
]}

Huang, Shuechin ^{[2
]}

机构：

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

[2] Dong Hwa Univ, Dept Appl Math, Hualien 97401, Taiwan

来源：

JOURNAL OF GLOBAL OPTIMIZATION | 2010年 / 46卷 / 04期

关键词：

Generalized vector variational inequality; Variable ordering relation; Cone mapping; KKM-Fan theorem; Brouwer fixed point theorem; Monotonicity; Complete continuity; REFLEXIVE BANACH-SPACES;

D O I：

10.1007/s10898-009-9436-9

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

In this paper we study the solvability of the generalized vector variational inequality problem, the GVVI problem, with a variable ordering relation in reflexive Banach spaces. The existence results of strong solutions of GVVIs for monotone multifunctions are established with the use of the KKM-Fan theorem. We also investigate the GVVI problems without monotonicity assumptions and obtain the corresponding results of weak solutions by applying the Brouwer fixed point theorem. These results are also the extension and improvement of some recent results in the literature.

引用

页码：521 / 535

页数：15

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