On generalized Peano and Peano derivatives

H. Fejzić

Fundamenta Mathematicae (1993)

  • Volume: 143, Issue: 1, page 55-74
  • ISSN: 0016-2736

Abstract

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A function F is said to have a generalized Peano derivative at x if F is continuous in a neighborhood of x and if there exists a positive integer q such that a qth primitive of F in the neighborhood has the (q+n)th Peano derivative at x; in this case the latter is called the generalized nth Peano derivative of F at x and denoted by F [ n ] ( x ) . We show that generalized Peano derivatives belong to the class [Δ’]. Also we show that they are path derivatives with a nonporous system of paths satisfying the I.I.C. condition as defined in [3]. This gives a new approach to studying generalized Peano and Peano derivatives since all their known properties can be obtained from the corresponding properties of path derivatives. Moreover, generalized Peano derivatives are selective derivatives.

How to cite

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Fejzić, H.. "On generalized Peano and Peano derivatives." Fundamenta Mathematicae 143.1 (1993): 55-74. <http://eudml.org/doc/211992>.

@article{Fejzić1993,
abstract = {A function F is said to have a generalized Peano derivative at x if F is continuous in a neighborhood of x and if there exists a positive integer q such that a qth primitive of F in the neighborhood has the (q+n)th Peano derivative at x; in this case the latter is called the generalized nth Peano derivative of F at x and denoted by $F_\{[n]\}(x)$. We show that generalized Peano derivatives belong to the class [Δ’]. Also we show that they are path derivatives with a nonporous system of paths satisfying the I.I.C. condition as defined in [3]. This gives a new approach to studying generalized Peano and Peano derivatives since all their known properties can be obtained from the corresponding properties of path derivatives. Moreover, generalized Peano derivatives are selective derivatives.},
author = {Fejzić, H.},
journal = {Fundamenta Mathematicae},
keywords = {composite derivatives; generalized Peano derivative; compact derivative; path derivative; selective derivative},
language = {eng},
number = {1},
pages = {55-74},
title = {On generalized Peano and Peano derivatives},
url = {http://eudml.org/doc/211992},
volume = {143},
year = {1993},
}

TY - JOUR
AU - Fejzić, H.
TI - On generalized Peano and Peano derivatives
JO - Fundamenta Mathematicae
PY - 1993
VL - 143
IS - 1
SP - 55
EP - 74
AB - A function F is said to have a generalized Peano derivative at x if F is continuous in a neighborhood of x and if there exists a positive integer q such that a qth primitive of F in the neighborhood has the (q+n)th Peano derivative at x; in this case the latter is called the generalized nth Peano derivative of F at x and denoted by $F_{[n]}(x)$. We show that generalized Peano derivatives belong to the class [Δ’]. Also we show that they are path derivatives with a nonporous system of paths satisfying the I.I.C. condition as defined in [3]. This gives a new approach to studying generalized Peano and Peano derivatives since all their known properties can be obtained from the corresponding properties of path derivatives. Moreover, generalized Peano derivatives are selective derivatives.
LA - eng
KW - composite derivatives; generalized Peano derivative; compact derivative; path derivative; selective derivative
UR - http://eudml.org/doc/211992
ER -

References

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