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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