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Point derivations for Lipschitz functions andClarke's generalized derivative

100%

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.

Bernstein and van der Corput-Schaake type inequalities on semialgebraic curves

88%

Baran M., Pleśniak W.

Studia Mathematica

1997

tom 125

nr 1

83-96

We show that in the class of compact, piecewise $C^1$ curves K in $ℝ^n$, the semialgebraic curves are exactly those which admit a Bernstein (or a van der Corput-Schaake) type inequality for the derivatives of (the traces of) polynomials on K.

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Delay perturbed evolution problems involving time dependent subdifferential operators

75%

Saïdi S., Yarou M.

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

2014

tom 34

nr 1

61-87

We investigate in the present paper, the existence and uniqueness of solutions for functional differential inclusions involving a subdifferential operator in the infinite dimensional setting. The perturbation which contains the delay is single-valued, separately measurable, and separately Lipschitz. We prove, without any compactness condition, that the problem has one and only one solution.

Ograniczanie wyników

1 Applicationes Mathematicae

1 Discussiones Mathematicae, Differential Inclusions, Control and Optimization

1 Studia Mathematica

1 Baran M.

1 Demyanov V. F.

1 Pallaschke D.

1 Pleśniak W.

1 Saïdi S.

1 Yarou M.

1 2014

2 1997

Wyniki wyszukiwania

Point derivations for Lipschitz functions andClarke's generalized derivative

Bernstein and van der Corput-Schaake type inequalities on semialgebraic curves

Delay perturbed evolution problems involving time dependent subdifferential operators