东北大学学报（自然科学版）

东北大学学报(自然科学版) ›› 2012, Vol. 33 ›› Issue (8): 1206-1208.DOI: -

• 论著 • 上一篇    下一篇

凸幂凝聚增或减算子的不动点

张国伟;张同山;   

  1. 东北大学理学院;
  • 收稿日期:2013-06-19 修回日期:2013-06-19 发布日期:2013-04-04
  • 通讯作者: -
  • 作者简介:-
  • 基金资助:
    辽宁省自然科学基金资助项目(201102070)

Fixed points of convex-power condensing increasing/decreasing operator

Zhang, Guo-Wei (1); Zhang, Tong-Shan (1)   

  1. (1) School of Sciences, Northeastern University, Shenyang 110819, China
  • Received:2013-06-19 Revised:2013-06-19 Published:2013-04-04
  • Contact: Zhang, G.-W.
  • About author:-
  • Supported by:
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摘要： 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.

关键词: 不动点, 凸幂凝聚, 增算子, 减算子

Abstract: 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.

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