Estimates of the remainder in Taylor’s theorem using the Henstock-Kurzweil integral

Talvila, Erik. "Estimates of the remainder in Taylor’s theorem using the Henstock-Kurzweil integral." Czechoslovak Mathematical Journal 55.4 (2005): 933-940. <http://eudml.org/doc/31000>.

@article{Talvila2005,
abstract = {When a real-valued function of one variable is approximated by its $n$th degree Taylor polynomial, the remainder is estimated using the Alexiewicz and Lebesgue $p$-norms in cases where $f^\{(n)\}$ or $f^\{(n+1)\}$ are Henstock-Kurzweil integrable. When the only assumption is that $f^\{(n)\}~$ is Henstock-Kurzweil integrable then a modified form of the $n$th degree Taylor polynomial is used. When the only assumption is that $f^\{(n)\}\in C^0$ then the remainder is estimated by applying the Alexiewicz norm to Schwartz distributions of order 1.},
author = {Talvila, Erik},
journal = {Czechoslovak Mathematical Journal},
keywords = {Taylor’s theorem; Henstock-Kurzweil integral; Alexiewicz norm; Taylor theorem; Henstock-Kurzweil integral; Alexiewicz norm},
language = {eng},
number = {4},
pages = {933-940},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Estimates of the remainder in Taylor’s theorem using the Henstock-Kurzweil integral},
url = {http://eudml.org/doc/31000},
volume = {55},
year = {2005},
}

TY - JOUR
AU - Talvila, Erik
TI - Estimates of the remainder in Taylor’s theorem using the Henstock-Kurzweil integral
JO - Czechoslovak Mathematical Journal
PY - 2005
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 55
IS - 4
SP - 933
EP - 940
AB - When a real-valued function of one variable is approximated by its $n$th degree Taylor polynomial, the remainder is estimated using the Alexiewicz and Lebesgue $p$-norms in cases where $f^{(n)}$ or $f^{(n+1)}$ are Henstock-Kurzweil integrable. When the only assumption is that $f^{(n)}~$ is Henstock-Kurzweil integrable then a modified form of the $n$th degree Taylor polynomial is used. When the only assumption is that $f^{(n)}\in C^0$ then the remainder is estimated by applying the Alexiewicz norm to Schwartz distributions of order 1.
LA - eng
KW - Taylor’s theorem; Henstock-Kurzweil integral; Alexiewicz norm; Taylor theorem; Henstock-Kurzweil integral; Alexiewicz norm
UR - http://eudml.org/doc/31000
ER -