弱向量变分不等式的解集及其连通性

建立Hausdorff拓扑向量空间的非空凸子集到其值域为连续线性映射空间L(X, Y) 内的C -单调映射的弱向量变分不等式和它的纯量型变分不等式问题解的存在性, 讨论该弱向量变分不等式与之相联系的纯量型变分不等式解集的关系, 利用映射的C -弱次连续和C -单调性及其集值映射的不动点定理,通过纯量型变分不等式解集所诱导的集值映射所具有的特性给出弱向量变分不等式解集的连通性.

The Solution Sets and Connectedness for Weak Vector Variational Inequalities

The existence and connectedness of solutions for weak vector variational inequalities and their scalarization with a C-monotone mapping from a topological vector space to continuous linear mapping space L(X, Y) are shown. With the C-weak hemicontinuity and C-monotonicity for a mapping, and setvalued mapping fixed point theorems, the connectedness are derived by discussing the properties of set-valued mapping induced by solution sets of a scalarization variational inequality related to the weak vector variational inequalities.