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Point derivations for Lipschitz functions andClarke's generalized derivative

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Demyanov V. F., Pallaschke D.

Applicationes Mathematicae

1996-1997

tom 24

nr 4

465-474

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.

Ograniczanie wyników

1 Applicationes Mathematicae

1 Demyanov V. F.

1 Pallaschke D.

1 1997

Wyniki wyszukiwania

Point derivations for Lipschitz functions andClarke's generalized derivative