A Note on Differentiability of Lipschitz Maps
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 58 (2010) no. 3, pp. 259-268
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
We show that every Lipschitz map defined on an open subset of the Banach space $C(K)$, where $K$ is a scattered compactum, with values in a Banach space with the Radon–Nikodym property, has a point of Fréchet differentiability. This is a strengthening of the result of Lindenstrauss and Preiss who proved that for countable compacta. As a consequence of the above and a result of Arvanitakis we prove that Lipschitz functions on certain function spaces are Gâteaux differentiable.
Keywords:
every lipschitz map defined subset banach space where scattered compactum values banach space radon nikodym property has point chet differentiability strengthening result lindenstrauss preiss who proved countable compacta consequence above result arvanitakis prove lipschitz functions certain function spaces teaux differentiable
Affiliations des auteurs :
Rafa/l Górak 1
Rafa/l Górak. A Note on Differentiability of Lipschitz Maps. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 58 (2010) no. 3, pp. 259-268. doi: 10.4064/ba58-3-8
@article{10_4064_ba58_3_8,
author = {Rafa/l G\'orak},
title = {A {Note} on {Differentiability} of {Lipschitz} {Maps}},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
pages = {259--268},
year = {2010},
volume = {58},
number = {3},
doi = {10.4064/ba58-3-8},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/ba58-3-8/}
}
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