RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mat. Zametki:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Mat. Zametki, 1976, Volume 19, Issue 3, Pages 313–322 (Mi mz7750)  

This article is cited in 3 scientific papers (total in 3 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
$$ \int_GP(x)f(x) dx\approx\sum_{\nu=1}^mc_\nu f(x^\nu) $$


Full text: PDF file (560 kB)

English version:
Mathematical Notes, 1976, 19:3, 187–193

Bibliographic databases:

UDC: 517.5
Received: 11.12.1974

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/mz7750}
\mathscinet{http://www.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}


Linking options:
  • http://mi.mathnet.ru/eng/mz7750
  • http://mi.mathnet.ru/eng/mz/v19/i3/p313

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. N. P. Korneichuk, “S. M. Nikol'skii and the development of research on approximation theory in the USSR”, Russian Math. Surveys, 40:5 (1985), 83–156  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. Proc. Steklov Inst. Math., 225 (1999), 148–155  mathnet  mathscinet  zmath
    3. Borodachov S., “Optimal Recovery of Three Times Differentiable Functions on a Convex Polytope Inscribed in a Sphere”, J. Approx. Theory, 234 (2018), 51–63  crossref  isi
  • Математические заметки Mathematical Notes
    Number of views:
    This page:242
    Full text:102
    First page:1

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020