凸幂凝聚增或减算子的不动点

在由正规锥导出的半序Banach空间中,讨论了凸幂凝聚增或减算子不动点的存在性.对于凸幂凝聚增算子是锥区间自映射的情形,证明了在锥区间中存在最大不动点和最小不动点的结论.对于凸幂凝聚减算子是锥映射的情形,在一定条件下证明了存在唯一正不动点的结论.在这两种情形中,均给出了收敛到不动点的迭代序列.

Fixed Points of Convex-Power Condensing Increasing/ Decreasing Operator

In partial ordered Banach space deduced by normal cone,the existence of fixed points is discussed for a convex-power condensing operator which is increasing or decreasing.It is proved that when the convex-power condensing increasing operator is self-mapping in a cone interval,there exist the maximal and minimal fixed points and that when the convex-power condensing decreasing operator is cone-mapping,there exists a unique positive fixed point under certain conditions.In both cases,the iterative sequences converging to the fixed points are given.