Differentiation of n-convex functions

H. Fejzić; R. E. Svetic; C. E. Weil

Fundamenta Mathematicae, Tome 209 (2010), p. 9-25 / Harvested from The Polish Digital Mathematics Library

Résumé

The main result of this paper is that if f is n-convex on a measurable subset E of ℝ, then f is n-2 times differentiable, n-2 times Peano differentiable and the corresponding derivatives are equal, and $f^{(n - 1)} = f_{(n - 1)}$ except on a countable set. Moreover $f_{(n - 1)}$ is approximately differentiable with approximate derivative equal to the nth approximate Peano derivative of f almost everywhere.

Publié le : 2010-01-01

Zbl 1202.26008

EUDML-ID : urn:eudml:doc:282761

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     title = {Differentiation of n-convex functions},
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H. Fejzić; R. E. Svetic; C. E. Weil. Differentiation of n-convex functions. Fundamenta Mathematicae, Tome 209 (2010) pp. 9-25. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm209-1-2/