# The non-coincidence of ordinary and Peano derivatives

Zoltán Buczolich; Clifford E. Weil

Mathematica Bohemica (1999)

- Volume: 124, Issue: 4, page 381-399
- ISSN: 0862-7959

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topBuczolich, Zoltán, and Weil, Clifford E.. "The non-coincidence of ordinary and Peano derivatives." Mathematica Bohemica 124.4 (1999): 381-399. <http://eudml.org/doc/248446>.

@article{Buczolich1999,

abstract = {Let $f H\subset \mathbb \{R\}\rightarrow \mathbb \{R\}$ 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.},

author = {Buczolich, Zoltán, Weil, Clifford E.},

journal = {Mathematica Bohemica},

keywords = {Peano derivatives; nowhere dense perfect sets; porosity; Peano derivatives; nowhere dense perfect sets; porosity},

language = {eng},

number = {4},

pages = {381-399},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {The non-coincidence of ordinary and Peano derivatives},

url = {http://eudml.org/doc/248446},

volume = {124},

year = {1999},

}

TY - JOUR

AU - Buczolich, Zoltán

AU - Weil, Clifford E.

TI - The non-coincidence of ordinary and Peano derivatives

JO - Mathematica Bohemica

PY - 1999

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 124

IS - 4

SP - 381

EP - 399

AB - Let $f H\subset \mathbb {R}\rightarrow \mathbb {R}$ 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.

LA - eng

KW - Peano derivatives; nowhere dense perfect sets; porosity; Peano derivatives; nowhere dense perfect sets; porosity

UR - http://eudml.org/doc/248446

ER -

## References

top- H. Fejzić J. Mařík C. E. Weil, Extending Peano derivatives, Math. Bohem. 119 (1994), 387-406. (1994) MR1316592
- 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. (1923)
- J. Mařík, Derivatives and closed sets, Acta. Math. Acad. Sci. Hungar. 43 (1998), 25-29. (1998) MR0731958
- Clifford E. Weil, The Peano notion of higher order differentiation, Math. Japonica 42 (1995), 587-600. (1995) MR1363850

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