Banach空间超空间上的Markov-Kakutani定理

IF 0.7 Q2 MATHEMATICS
Shueh-Inn Hu, Thakyin Hu
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引用次数: 0

摘要

假设$X$是一个Banach空间,$K$是$X$的紧凸子集。设$\mathcal{F}$是$K$到$K$的连续仿射映射的交换族。由Markov-Kakutani定理可知$\mathcal{F}$在$K$中有一个公共不动点。现在假设$(CC(X), h)$是$X$的对应超空间,它包含了$X$的所有紧的,凸的子集,赋予了Hausdorff度量$h$。我们将证明上述版本的Markov-Kakutani定理在超空间$(CC(X), h)$上是有效的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Markov-Kakutani Theorem on Hyperspace of a Banach Space
Suppose $X$ is a Banach space and $K$ is a compact convex subset of $X$. Let $\mathcal{F}$ be a commutative family of continuous affine mappings of $K$ into $K$. It follows from Markov-Kakutani Theorem that $\mathcal{F}$ has a common fixed point in $K$. Suppose now $(CC(X), h)$ is the corresponding hyperspace of $X$ containing all compact, convex subsets of $X$ endowed with Hausdorff metric $h$. We shall prove the above version of Markov-Kakutani Theorem is valid on the hyperspace $(CC(X), h)$.
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来源期刊
CiteScore
1.50
自引率
0.00%
发文量
11
期刊介绍: To promote research interactions between local and overseas researchers, the Department has been publishing an international mathematics journal, the Tamkang Journal of Mathematics. The journal started as a biannual journal in 1970 and is devoted to high-quality original research papers in pure and applied mathematics. In 1985 it has become a quarterly journal. The four issues are out for distribution at the end of March, June, September and December. The articles published in Tamkang Journal of Mathematics cover diverse mathematical disciplines. Submission of papers comes from all over the world. All articles are subjected to peer review from an international pool of referees.
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