TY - JOUR
AU - Hu, Shueh-Inn
AU - Hu, Thakyin
PY - 2021/01/31
Y2 - 2021/06/25
TI - Markov-Kakutani Theorem on Hyperspace of a Banach Space
JF - Tamkang Journal of Mathematics
JA - Tamkang J. Math.
VL - 52
IS - 1
SE -
DO - 10.5556/j.tkjm.52.2021.3645
UR - https://journals.math.tku.edu.tw/index.php/TKJM/article/view/3645
SP - 19-23
AB - <p>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 $(CC(X), h)$.</p>
ER -