Geodesic
Point derivations for Lipschitz functions andClarke's generalized derivative
Applicationes Mathematicae, Tome 24 (1997) no. 4, pp. 465-474.

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Clarke's generalized derivative $f^0(x,v)$ 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 $x\in X$ and fixed $v\in E$ the function $f^0(x,v)$ is continuous and sublinear in $f\in Lip(X,d)$. 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.
DOI : 10.4064/am-24-4-465-474
Keywords: point derivations, generalized directional derivative, Lipschitz functions

Vladimir Demyanov 1 ; Diethard Pallaschke 1

1 
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Vladimir Demyanov; Diethard Pallaschke. Point derivations for Lipschitz functions andClarke's generalized derivative. Applicationes Mathematicae, Tome 24 (1997) no. 4, pp. 465-474. doi : 10.4064/am-24-4-465-474. http://geodesic.mathdoc.fr/articles/10.4064/am-24-4-465-474/

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