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

Title:

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

Creator:

Talvila, Erik

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:9c508fd8-ddbf-4e6e-a4a2-6bb1d96da314
uuid:9c508fd8-ddbf-4e6e-a4a2-6bb1d96da314

Subject:

Taylor’s theorem, Henstock-Kurzweil integral, and Alexiewicz norm

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

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.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

933-940

Source:

Czechoslovak Mathematical Journal | 2005 Volume:55 | Number:4

Harvested from:

CDK

Metadata only:

false