Hölder continuous retractions and amenable semigroups of uniformly Lipschitzian mappings in Hilbert spaces
Keywords
Amenable semigroup, uniformly Lipschitzian mapping, Hölder continuous retraction, fixed pointAbstract
Suppose that $S$ is a left amenable semitopological semigroup. We prove that if $\mathcal{S}=\{ T_{t}:t\in S\} $ is a uniformly $k$-Lipschitzian semigroup on a bounded closed and convex subset $C$ of a Hilbert space and $k< \sqrt{2}$, then the set of fixed points of $\mathcal{S}$ is a Hölder continuous retract of $C$. This gives a qualitative complement to the Ishihara-Takahashi fixed point existence theorem.Downloads
Published
2016-04-12
How to Cite
1.
WIŚNICKI, Andrzej. Hölder continuous retractions and amenable semigroups of uniformly Lipschitzian mappings in Hilbert spaces. Topological Methods in Nonlinear Analysis. Online. 12 April 2016. Vol. 43, no. 1, pp. 89 - 96. [Accessed 25 April 2024].
Issue
Section
Articles
Stats
Number of views and downloads: 0
Number of citations: 0