抽象凸空间上类K的性质及聚合不动点定理

给出抽象凸空间上映射类K的两个性质, 利用已知抽象凸空间上的重叠点定理讨论抽象凸空间上映射的不动点存在问题, 得到了若干新的不动点定理, 同时进一步给出了抽象凸空间族的乘积空间上映射族的聚合不动点定理.

Properties of Class K and Collectively Fixed Point Theorems on Abstract Convex Spaces

We first gave two properties of map class K on Abstract convex spaces,and then used the well-known coincidence point theorem on Abstract convex spaces to discuss the existence problem of fixed points for maps on Abstract convex spaces and obtained some new fixed point theorems,from which several collectively fixed point theorems were established for a family of maps on a product space of a family of Abstract convex spaces.