## Topological Methods in Nonlinear Analysis

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

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

#### 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