Hölder continuous retractions and amenable semigroups of uniformly Lipschitzian mappings in Hilbert spaces
Słowa kluczowe
Amenable semigroup, uniformly Lipschitzian mapping, Hölder continuous retraction, fixed pointAbstrakt
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.Pobrania
Opublikowane
2016-04-12
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1.
WIŚNICKI, Andrzej. Hölder continuous retractions and amenable semigroups of uniformly Lipschitzian mappings in Hilbert spaces. Topological Methods in Nonlinear Analysis [online]. 12 kwiecień 2016, T. 43, nr 1, s. 89–96. [udostępniono 22.7.2024].
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