东北大学学报（自然科学版）

东北大学学报(自然科学版) ›› 2013, Vol. 34 ›› Issue (4): 602-604.DOI: -

• 数学·物理 • 上一篇    下一篇

Altman型不动点定理的一些注记

张国伟，张秀萍   

  1. (东北大学理学院，辽宁沈阳110819)
  • 收稿日期:2012-10-15 修回日期:2012-10-15 出版日期:2013-04-15 发布日期:2013-06-19
  • 通讯作者: 张国伟
  • 作者简介:张国伟(1965-)，男，辽宁沈阳人，东北大学教授，博士.
  • 基金资助:
    辽宁省自然科学基金资助项目(201102070).

Some Notes on Fixed Point Theorems of AltmanType

ZHANG Guowei， ZHANG Xiuping   

  1. School of Sciences， Northeastern University， Shenyang 110819， China.
  • Received:2012-10-15 Revised:2012-10-15 Online:2013-04-15 Published:2013-06-19
  • Contact: ZHANG Guowei
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摘要： 针对Altman型不动点定理，讨论了在第一个指数参数分别大于1和在0和1之间，而第二个指数参数不小于0指数情形范数不等式条件下全连续算子不动点的存在性.证明了几个新的不动点定理.这些不等式条件与文献中已有条件不同，推广和补充了这些文献中的结果.结论对于更一般的半闭1-集压缩、凸幂凝聚和半闭凸幂1-集压缩算子也是成立的.

关键词: 不动点, 全连续算子, 1-集压缩, 凸幂凝聚, 凸幂1-集压缩

Abstract: Fixed point theorems of Altmantype were studied. The existence of the fixed point of completely continuous operator was discussed under the norm inequality conditions that the first exponent parameter was respectively greater than 1 and between 0 and 1， at the same time， the second one was not less than 0. Some new fixed point theorems were proved. These inequality conditions were different from those as shown in earlier works in which the results were extended and supplemented. The conclusions were valid for more general operators such as semiclosed 1setcontraction， convexpower condensing operator and semiclosed convexpower 1setcontraction in references.

Key words: fixed point, completely continuous operator, 1setcontraction, convexpower condensing, convexpower 1setcontraction

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