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Zbl 1146.47034
Matkowski, Janusz
Remarks on Lipschitzian mappings and some fixed point theorems.
(English)
[J] Banach J. Math. Anal. 1, No. 2, 237-244, electronic only (2007). ISSN 1735-8787/e

Let $X$ and $Y$ be normed spaces, $C$ be a convex subset of $X$ and let $T: C\to Y$ be a continuous mapping. Then, under some additional conditions about $T$, some results saying that $T$ is a Lipschitzian mapping are presented. These results are applied to a mapping defined on a subset of a uniformly convex Banach space to get some fixed point theorems.
[Stefan Czerwik (Gliwice)]
MSC 2000:
*47H10 Fixed point theorems for nonlinear operators on topol.linear spaces
54H25 Fixed-point theorems in topological spaces

Keywords: Lipschitz mapping; fixed point

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