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Mat. Tr., 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

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.

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English version:
Siberian Advances in Mathematics, 2015, 25:1, 56–75

Bibliographic databases:

Document Type: Article
UDC: 517
Received: 24.06.2013

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://www.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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    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. Yu. G. Nikonorov, “Peano's theorem and coplanarity points of space curves”, Siberian Adv. Math., 25:2 (2015), 124–137  mathnet  crossref  mathscinet
  • Математические труды Siberian Advances in Mathematics
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