请输入您要查询的字词:

 

单词 SchauderFixedPointTheorem
释义

Schauder fixed point theorem


Let X be a normed vector spacePlanetmathPlanetmath, and let KX be a non-empty, compactPlanetmathPlanetmath, and convex set.Then given any continuous mapping f:KKthere exists xK such that f(x)=x.

Notice that the unit disc of a finite dimensional vector space is always convex and compact hence this theorem extends Brouwer Fixed Point TheoremMathworldPlanetmath.

Notice that the space X is not required to be completePlanetmathPlanetmathPlanetmath, however the subset K being compact,is complete with respect to the metric induced by X.

References

  • 1 Rudin, Functional AnalysisMathworldPlanetmath, Chapter 5.
随便看

 

数学辞典收录了18232条数学词条,基本涵盖了常用数学知识及数学英语单词词组的翻译及用法,是数学学习的有利工具。

 

Copyright © 2000-2023 Newdu.com.com All Rights Reserved
更新时间:2025/5/4 11:11:59