Application of Upper Hemi-Continuous Operators on Generalized Bi-quasi-variational Inequalities in Locally Convex Topological Vector Spaces期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Application of Upper Hemi-Continuous Operators on Generalized Bi-quasi-variational Inequalities in Locally Convex Topological Vector Spaces

Authors:	Chowdhury Mohammad S R Tan Kok-Keong

Institution:	(1) Department of Mathematics, The University of Queensland, Brisbane, Queensland, 4072, Australia;(2) Department of Mathematics and Statistics, Dalhousie University, Halifax, Nova Scotia, Canada, B3H 3J5

Abstract:	Let and be Hausdorff topological vector spaces over the field $\Phi$ , let $\left\langle , \right\rangle :F \times E \to \Phi$ be a bilinear functional, and let be a non-empty subset of . Given a set-valued map $S:X \to 2^X$ and two set-valued maps $M,T:X \to 2^F$ , the generalized bi-quasi-variational inequality (GBQVI) problem is to find a point $\hat y \in X$ and a point $\hat w \in T(\hat y)$ such that $\hat y \in S(\hat y)$ and $\operatorname{Re} \left\langle {f - \hat w,\hat y - x} \right\rangle \leqslant 0$ for all $x \in S(\hat y)$ and for all $f \in M(\hat y)$ or to find a point $\hat y \in X,$ a point $\hat w \in T(\hat y)$ and a point $\hat f \in M(\hat y)$ such that $\hat y \in S(\hat y)$ and $\operatorname{Re} \left\langle {\hat f - \hat w,\hat y - x} \right\rangle \leqslant 0$ for all $x \in S(\hat y)$ . The generalized bi-quasi-variational inequality was introduced first by Shih and Tan 8] in 1989. In this paper we shall obtain some existence theorems of generalized bi-quasi-variational inequalities as application of upper hemi-continuous operators 4] in locally convex topological vector spaces on compact sets.

Keywords:	Bilinear functional generalized bi-quasi-variational inequality locally convex space lower semicontinuous upper semicontinuous upper hemi-continuous monotone and semi-monotone operators
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