| Summary: | 碩士 === 國立彰化師範大學 === 數學研究所 === 86 ===
In this paper, we consider a vector quasi-variational inequality for multimaps on convex subset of locally convex topological vector space and es-tablish the existence theorems.
1. Introduction
We let X and Y be topological spaces, Z be a real t.v.s. with a closed convex cone D, such that intD ≠ □,S : X-oX, G : X *Y * X -oZ, T : X@oY. We will consider the vector quasi-variational inequalities (VQVI) for multimaps;(VQVI) Find x εS(x) and y εT(x), such that for any x εS(x), any z εG(x,y,x),z □ -int D.
Giannessi [3] first introduced a vector variational inequality for vector-valued functions in a finite-dimensional Euclidean space. Recently, many authors (Lee et al. [8,9] and Lin [10,11]) have studied sevseal kinds of vector variational inequalities for vector-valued functions or vector-valued multimaps in abstract spaces.
In this paper, we use continuous selection theorem of Horvath [4], the continuous property of Lin [13] and some fixed points theorems of Park [16], Browder [2] and ldzik [5] to establish the existence theorems for the vector quasi-variational inequalities for multimaps. Finally, our results extened Wu [17] and many others.
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