乘积空间中凹泛函型锥拉伸与压缩不动点定理

doi:10.12068/j.issn.1005-3026.2015.02.032

东北大学学报:自然科学版 ›› 2015, Vol. 36 ›› Issue (2): 301-304.DOI: 10.12068/j.issn.1005-3026.2015.02.032

• 数学 • 上一篇

乘积空间中凹泛函型锥拉伸与压缩不动点定理

张国伟，张秀萍

(东北大学理学院，辽宁沈阳110819)

收稿日期:2013-11-29 修回日期:2013-11-29 出版日期:2015-02-15 发布日期:2014-11-07
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.
基金资助:
辽宁省自然科学基金资助项目(201102070).

Fixed Point Theorems of Cone Expansion and Compression of Concave Functional Type in Product Space

ZHANG Guo-wei， ZHANG Xiu-ping

School of Sciences， Northeastern University， Shenyang 110819， China.

Received:2013-11-29 Revised:2013-11-29 Online:2015-02-15 Published:2014-11-07
Contact: ZHANG Guo-wei
About author:-
Supported by:
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摘要/Abstract

摘要： 考虑赋范线性空间的乘积空间，由因子空间中的锥生成乘积空间中的锥. 全连续算子定义在乘积空间中锥与两个闭球相交得到的有界闭集上，并且值域在锥中. 在由锥上一类非负正齐次凹泛函表示的混合型锥拉伸与压缩条件下，利用构造性方法将其转化为Schauder型问题，证明了几个全连续算子的不动点定理. 通过例子说明这里所需要的凹泛函在常用的空间及其锥上是容易构造的.

关键词: 不动点, 全连续算子, 锥拉伸与压缩, 凹泛函, 乘积空间

Abstract: A product space of normed linear spaces is considered， and the cone in the product space is produced by the cones in its factor spaces. A completely continuous operator is in the product space defined on the bounded closed set which is the intersection of the cone with two closed balls， and the range is in the cone. Under the mixed cone expansion and compression conditions that are expressed through a class of nonnegative， positively homogeneous， concave functionals on the cone， some fixed point theorems about the completely continuous operator are proved by constructing methods and converting them into the problems of Schauder type. It is illustrated by example that the concave functionals needed here are easily constructed in a common space and on a cone in it.

Key words: fixed point, completely continuous operator, cone expansion and compression, concave functional, product space

中图分类号:

O177. 91

张国伟，张秀萍. 乘积空间中凹泛函型锥拉伸与压缩不动点定理[J]. 东北大学学报:自然科学版, 2015, 36(2): 301-304.

ZHANG Guo-wei， ZHANG Xiu-ping. Fixed Point Theorems of Cone Expansion and Compression of Concave Functional Type in Product Space[J]. Journal of Northeastern University Natural Science, 2015, 36(2): 301-304.

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乘积空间中凹泛函型锥拉伸与压缩不动点定理

Fixed Point Theorems of Cone Expansion and Compression of Concave Functional Type in Product Space

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