一般化凸空间上变分不等式解的存在定理

Existence theorems of solutions for variational inequalities on generalized convex spaces

根据已知的KKM型定理得出一般化凸空间上变分不等式的择一性定理,利用拓扑空间X的积空间X×X上的实值函数,构造出一个G-凸空间,并在该空间上讨论变分不等式解的存在问题.

The well-known KKM type theorem was used to obtain alternative theorems of variational inequalities on generalizded convex spaces, and then a generalizded convex space was constructed by using a real function on product space X × X of a topological space X and the existence problems of solutions for variational inequalities were discussed on this space.