局部凸拓扑矢量空间内的广义拟变分不等式

设X是局部凸空间E的仿紧凸子集 ,F :X→ 2 X 是集值映象 ,φ :X×X→R是实泛函 .研究下列抽象广义拟变分不等式 (AGQVI) :求 ^x∈X使得 ^x∈F(^x)和 φ(^x ,y)≤ 0 , y∈F(^x) ,其中 φ(x ,y)关于x是 0 转移紧下半连续的和关于y是 0 对角拟凹的 .作为应用 ,作者得到了最近文献中关于广义拟变分不等式的很多已知结果的推广 .

Generalized Quasi-variational Inequalities in Locally Convex Topological Vector Spaces

Let X be a paracompact convex subset of a locally convex space E, F:X→2X be a set-valued mapping and φ:X×X→R be a real function. We study the following abstract generalized quasi-variational inequality (AGQVI): finding ∈X such that ∈F() and φ(,y)0, y∈F(), where the φ(x,y) is 0-transfer compactly lower semicontinuous in x and 0-iagonally quasi-concave in y. Applying this result, we obtain some generalizations of many known results for generalized quasi-variational inequalities in recent literature. Keywords：Abstract generalized quasi-variational inequality; Locally convex space; 0-transfer compactly lower (upper) semicontinuous; 0-diagonally quasi-concave (quasiconvex)