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

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dc.creatorTalvila, Erik
dc.date2004-06-18
dc.date.accessioned2026-07-07T05:09:22Z
dc.date.available2026-07-07T05:09:22Z
dc.descriptionWhen 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.
dc.descriptionTo appear in Czechoslovak Mathematical Journal
dc.identifierhttps://arxiv.org/abs/math/0406372
dc.identifierhttp://arxiv.org/abs/math/0406372
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/71605
dc.subjectClassical Analysis and ODEs
dc.subject26A24; 26A39
dc.titleEstimates of the remainder in Taylor's theorem using the Henstock--Kurzweil integral
dc.typetext

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