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Matematicheskie Trudy, 2014, Volume 17, Number 1, Pages 145–174 (Mi mt271)  

This article is cited in 1 scientific paper (total in 1 paper)

Asymptotics of mean value points in the Schwarz theorem for divided differences

Yu. G. Nikonorov

South Mathematical Institute of VSC RAS, Vladikavkaz, Russia
Full-text PDF (324 kB) Citations (1)
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Abstract: We establish inequalities describing the asymptotic behavior of mean value points in the sense of the Schwarz theoremfor general divided differences constructed for a function with a certain growth order at a given point. These inequalities generalize a number of known results, in particular, of ones connected with the asymptotics of Lagrange points in the Taylor formula.
Key words: divided difference, Schwarz theorem, mean value theorem, $B$-spline, Peano kernel, asymptotics of mean value points.
Received: 24.06.2013
English version:
Siberian Advances in Mathematics, 2015, Volume 25, Issue 1, Pages 56–75
DOI: https://doi.org/10.3103/S105513441501006X
Bibliographic databases:
Document Type: Article
UDC: 517
Language: Russian
Citation: Yu. G. Nikonorov, “Asymptotics of mean value points in the Schwarz theorem for divided differences”, Mat. Tr., 17:1 (2014), 145–174; Siberian Adv. Math., 25:1 (2015), 56–75
Citation in format AMSBIB
\Bibitem{Nik14}
\by Yu.~G.~Nikonorov
\paper Asymptotics of mean value points in the Schwarz theorem for divided differences
\jour Mat. Tr.
\yr 2014
\vol 17
\issue 1
\pages 145--174
\mathnet{http://mi.mathnet.ru/mt271}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3236365}
\transl
\jour Siberian Adv. Math.
\yr 2015
\vol 25
\issue 1
\pages 56--75
\crossref{https://doi.org/10.3103/S105513441501006X}
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  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математические труды Siberian Advances in Mathematics
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    Abstract page:336
    Full-text PDF :96
    References:64
    First page:13
     
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