Geodesic
A Note on Differentiability of Lipschitz Maps
Rafa/l Górak1
1 Technical University of Warsaw Pl. Politechniki 1 00-661 Warszawa, Poland
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 58 (2010) no. 3, pp. 259-268 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

Voir la notice de l'article

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.
DOI : 10.4064/ba58-3-8
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

Rafa/l Górak 1

1 Technical University of Warsaw Pl. Politechniki 1 00-661 Warszawa, Poland 
@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/}
}
TY  - JOUR
AU  - Rafa/l Górak
TI  - A Note on Differentiability of Lipschitz Maps
JO  - Bulletin of the Polish Academy of Sciences. Mathematics
PY  - 2010
SP  - 259
EP  - 268
VL  - 58
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4064/ba58-3-8/
DO  - 10.4064/ba58-3-8
LA  - en
ID  - 10_4064_ba58_3_8
ER  - 
%0 Journal Article
%A Rafa/l Górak
%T A Note on Differentiability of Lipschitz Maps
%J Bulletin of the Polish Academy of Sciences. Mathematics
%D 2010
%P 259-268
%V 58
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4064/ba58-3-8/
%R 10.4064/ba58-3-8
%G en
%F 10_4064_ba58_3_8
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

Cité par Sources :