Geodesic
The non-coincidence of ordinary and Peano derivatives
Mathematica Bohemica, Tome 124 (1999) no. 4, pp. 381-399

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MR Zbl
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.
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.
DOI : 10.21136/MB.1999.125997
Classification : 26A24
Keywords: Peano derivatives; nowhere dense perfect sets; porosity 
Buczolich, Zoltán; Weil, Clifford E. The non-coincidence of ordinary and Peano derivatives. Mathematica Bohemica, Tome 124 (1999) no. 4, pp. 381-399. doi: 10.21136/MB.1999.125997
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[1] H. Fejzić J. Mařík C. E. Weil: Extending Peano derivatives. Math. Bohem. 119 (1994), 387-406. | MR

[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

[4] Clifford E. Weil: The Peano notion of higher order differentiation. Math. Japonica 42 (1995), 587-600. | MR

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