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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On sequences of $C^{k,\delta}_{b}$ maps which converge in the uniform $C^{0}$-norm


Author: Mohamed Sami ElBialy
Journal: Proc. Amer. Math. Soc. 128 (2000), 3285-3290
MSC (2000): Primary 37D10
Published electronically: April 28, 2000
MathSciNet review: 1709749
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Abstract:

We study maps $f\in C^{k,\delta}_{b}(U,Y)$ and give detailed estimates on $\Vert D^{k}f(x)\Vert,x\in U,$ in terms of $\Vert f\Vert$ and $\Vert f\Vert _{k,\delta}$. These estimates are used to prove a lemma by D. Henry for the case $k\geq 2$. Here $U\subset X$ is an open subset and $X$ and $Y$ are Banach spaces.


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Additional Information

Mohamed Sami ElBialy
Affiliation: Department of Mathematics, University of Toledo, Toledo, Ohio 43606
Email: melbialy@math.utoledo.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05640-9
PII: S 0002-9939(00)05640-9
Keywords: Invariant manifolds, linearization, Henry's lemma
Received by editor(s): December 18, 1998
Published electronically: April 28, 2000
Communicated by: Michael Handel
Article copyright: © Copyright 2000 American Mathematical Society