# A Note on Differentiability of Lipschitz Maps

Bulletin of the Polish Academy of Sciences. Mathematics (2010)

- Volume: 58, Issue: 3, page 259-268
- ISSN: 0239-7269

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topRafał Górak. "A Note on Differentiability of Lipschitz Maps." Bulletin of the Polish Academy of Sciences. Mathematics 58.3 (2010): 259-268. <http://eudml.org/doc/281216>.

@article{RafałGórak2010,

abstract = {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.},

author = {Rafał Górak},

journal = {Bulletin of the Polish Academy of Sciences. Mathematics},

keywords = {scattered compactum; point of Fréchet differentiability; Lipschitz functions},

language = {eng},

number = {3},

pages = {259-268},

title = {A Note on Differentiability of Lipschitz Maps},

url = {http://eudml.org/doc/281216},

volume = {58},

year = {2010},

}

TY - JOUR

AU - Rafał Górak

TI - A Note on Differentiability of Lipschitz Maps

JO - Bulletin of the Polish Academy of Sciences. Mathematics

PY - 2010

VL - 58

IS - 3

SP - 259

EP - 268

AB - 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.

LA - eng

KW - scattered compactum; point of Fréchet differentiability; Lipschitz functions

UR - http://eudml.org/doc/281216

ER -

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