半序空间中一类非连续增算子的不动点定理

Fixed point theorem for a class of discontinuous increasing operators in the partially ordered spaces

将增算子A写成∑mi=1CiBi形式,讨论了此种类型算子在半序空间X中的不动点定理.通过对半序拓扑空间Yi中的相对紧性的讨论,并利用半序方法得到了A在X中存在最大与最小不动点的结论.

This paper mainly deals with the existence of fixed points for a kind of increasing operator A=∑mi=1CiBi in a partially ordered space X.By introducing the relative compactness in Yi and partially order method,the existence of the maximum and minimum fixed points in X is proved.