Markov-Kakutani Theorem on Hyperspace of a Banach Space

Authors

DOI:

https://doi.org/10.5556/j.tkjm.52.2021.3645

Keywords:

Markov-Kakutani theorem, Common fixed point, Hyperspace.

Abstract

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 $(CC(X), h)$.

References

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Published

2021-01-31

How to Cite

Hu, S.-I., & Hu, T. (2021). Markov-Kakutani Theorem on Hyperspace of a Banach Space. Tamkang Journal of Mathematics, 52(1), 19-23. https://doi.org/10.5556/j.tkjm.52.2021.3645