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Buczolich, Zoltán ; Weil, Clifford E.
The non-coincidence of ordinary and Peano derivatives. (English). Mathematica Bohemica, vol. 124 (1999), issue 4, pp. 381-399
MSC: 26A24 | MR 1722874 | Zbl 0936.26002 | DOI: 10.21136/MB.1999.125997
Keywords:
Peano derivatives; nowhere dense perfect sets; porosity
Summary:
Let $f H\subset\Bbb R\to\Bbb R$ be $k$ times differentiable in both the usual (iterative) and Peano senses. We investigate when the usual derivatives and the corresponding Peano derivatives are different and the nature of the set where they are different.
References:
[1] H. Fejzić J. Mařík C. E. Weil: Extending Peano derivatives. Math. Bohem. 119 (1994), 387-406. MR 1316592
[2] V. Jarník: Sur l'extension du domaine de definition des fonctions d'une variable, qui laisse intacte la derivabilité de la fonction. Bull international de l'Acad Sci de Boheme, 1923.
[3] J. Mařík: Derivatives and closed sets. Acta. Math. Acad. Sci. Hungar. 43 (1998), 25-29. MR 0731958
[4] Clifford E. Weil: The Peano notion of higher order differentiation. Math. Japonica 42 (1995), 587-600. MR 1363850
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