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Matematicheskie Zametki, 1976, Volume 19, Issue 3, Pages 313–322 (Mi mzm7750)  

This article is cited in 11 scientific papers (total in 11 papers)

Asymptotically sharp bounds for the remainder for the best quadrature formulas for several classes of functions

V. F. Babenko

Dnepropetrovsk State University
Abstract: For certain classes of functions (all functions are defined on a Jordan measurable set $G$) defined by a majorant on the modulus of continuity, we find an asymptotically sharp bound for the remainder of an optimal quadrature formula of the form
$$ \int_Gf(x)\,dx\approx\sum_{\nu=1}^mc_\nu f(x^\nu) $$
When the given majorant of the modulus of continuity is $t^\alpha$ and the nonnegative function $P(x)$ is such that for any nonnegative numbera the set $\{x\in G:P(x)\le a\}$ is Jordan measurable, then we also find an asymptotically sharp bound for the remainder of an optimal quadrature formula of the form
$$ \int_GP(x)f(x)\,dx\approx\sum_{\nu=1}^mc_\nu f(x^\nu) $$
Received: 11.12.1974
English version:
Mathematical Notes, 1976, Volume 19, Issue 3, Pages 187–193
DOI: https://doi.org/10.1007/BF01437850
Bibliographic databases:
UDC: 517.5
Language: Russian
Citation: V. F. Babenko, “Asymptotically sharp bounds for the remainder for the best quadrature formulas for several classes of functions”, Mat. Zametki, 19:3 (1976), 313–322; Math. Notes, 19:3 (1976), 187–193
Citation in format AMSBIB
\Bibitem{Bab76}
\by V.~F.~Babenko
\paper Asymptotically sharp bounds for the remainder for the best quadrature formulas for several classes of functions
\jour Mat. Zametki
\yr 1976
\vol 19
\issue 3
\pages 313--322
\mathnet{http://mi.mathnet.ru/mzm7750}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=417647}
\zmath{https://zbmath.org/?q=an:0333.41024}
\transl
\jour Math. Notes
\yr 1976
\vol 19
\issue 3
\pages 187--193
\crossref{https://doi.org/10.1007/BF01437850}
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  • https://www.mathnet.ru/eng/mzm/v19/i3/p313
  • This publication is cited in the following 11 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математические заметки Mathematical Notes
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