拓扑空间上不动点和具有上下界的变分不等式

Fixed Points and Variational Inequalities with Lower and Upper Bounds in Topological Spaces

根据广义凸空间上的KKM型定理和Fan-Browder型不动点定理,得到了没有凸和线性结构且没有紧致框架的拓扑空间上的Φ-映射和弱Φ-映射的若干个新的不动点定理.作为应用,在非紧致的拓扑空间上讨论了具有上下界的变分不等式解的存在性问题.

Based on an KKM type theorem and a Fan-Browder type fixed point theorem on generalized convex space, some new fixed point theorems for a φ-map and a weak φ-map defined on topological spaces without any convex and linear structure and any compact setting are obtained. As applications, some existence problems of solutions for variational inequalities with lower and upper bounds were discussed in non-compact topological spaces.