Clarke’s generalized derivative is studied as a function on the Banach algebra Lip(X,d) of bounded Lipschitz functions f defined on an open subset X of a normed vector space E. For fixed and fixed the function is continuous and sublinear in . It is shown that all linear functionals in the support set of this continuous sublinear function satisfy Leibniz’s product rule and are thus point derivations. A characterization of the support set in terms of point derivations is given.
@article{bwmeta1.element.bwnjournal-article-zmv24i4p465bwm,
author = {Vladimir Demyanov and Diethard Pallaschke},
title = {Point derivations for Lipschitz functions andClarke's generalized derivative},
journal = {Applicationes Mathematicae},
volume = {24},
year = {1997},
pages = {465-474},
zbl = {0916.49013},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-zmv24i4p465bwm}
}
Demyanov, Vladimir; Pallaschke, Diethard. Point derivations for Lipschitz functions andClarke's generalized derivative. Applicationes Mathematicae, Tome 24 (1997) pp. 465-474. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-zmv24i4p465bwm/
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