Strict feasibility for generalized mixed variational inequality in reflexive Banachspaces

Ren-You Zhong; Nan-Jing Huang

doi:10.3934/naco.2011.1.261

Article Contents

2011, Volume 1, Issue 2: 261-274. Doi: 10.3934/naco.2011.1.261

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Strict feasibility for generalized mixed variational inequality in reflexive Banach spaces

Ren-You Zhong^1, and
Nan-Jing Huang^1,

1.
Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064

Received: November 2010

Revised: March 2011

Published: May 2011

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Abstract

The purpose of this paper is to investigate the nonemptiness and boundedness of solution set for a generalized mixed variational inequality problem with strict feasibility in reflexive Banach spaces. We introduce a concept of strict feasibility for the generalized mixed variational inequality problem which includes the existing concepts of strict feasibility introduced for variational inequalities and complementarity problems. By using a degree theory developed in Wang and Huang [28], we prove that the monotone generalized mixed variational inequality has a nonempty bounded solution set if and only if it is strictly feasible. The results presented in this paper generalize and extend some known results in [8, 23].

Keywords:

Generalized mixed variational inequality,
topological degree,
generalized $f$-projection operator,
set-valued mapping.

Mathematics Subject Classification: Primary: 49J40; Secondary: 49J53.

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