Topological Methods in Nonlinear Analysis

Hölder continuous retractions and amenable semigroups of uniformly Lipschitzian mappings in Hilbert spaces

Andrzej Wiśnicki

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Abstract

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.

Article information

Source
Topol. Methods Nonlinear Anal., Volume 43, Number 1 (2014), 89-96.

Dates
First available in Project Euclid: 11 April 2016

Permanent link to this document
https://projecteuclid.org/euclid.tmna/1460381549

Mathematical Reviews number (MathSciNet)
MR3236601

Zentralblatt MATH identifier
06700743

Citation

Wiśnicki, Andrzej. Hölder continuous retractions and amenable semigroups of uniformly Lipschitzian mappings in Hilbert spaces. Topol. Methods Nonlinear Anal. 43 (2014), no. 1, 89--96. https://projecteuclid.org/euclid.tmna/1460381549


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