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- Title
Markov-Kakutani Theorem on Hyperspace of a Banach Space.
- Authors
Shueh-Inn Hu, Jennifer; Thakyin Hu
- Abstract
Suppose X is a Banach space and K is a compact convex subset of X. Let F be a commutative family of continuous affine mappings of K into K. It follows from Markov-Kakutani Theorem that 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).
- Subjects
HYPERSPACE; BANACH spaces; HAUSDORFF spaces; MARKOV processes; FIXED point theory
- Publication
Tamkang Journal of Mathematics, 2021, Vol 52, Issue 1, p19
- ISSN
0049-2930
- Publication type
Article
- DOI
10.5556/j.tkjm.52.2021.3645