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Mat. Tr., 2011, Volume 14, Number 1, Pages 141–157 (Mi mt210)  

This article is cited in 3 scientific papers (total in 3 papers)

Asymptotics of tangent points for planar curves

Yu. G. Nikonorovab

a South Mathematical Institute of VSC RAS, Vladikavkaz, Russia
b Volgodonsk Institute of Service (branch) of South-Russian State University of Economics and Service, Volgodonsk, Russia

Abstract: In this paper, we prove a universal inequality described the asymptotic behavior of tangent points for differentiable planar curves. As corollaries, we obtain some (partially known) assertions on the asymptotics of mean value points for a number of the classical theorems in analysis. We formulate some unsolved problems.

Key words: parametric curves in the plane, rectifiable curves, smooth curves, mean value theorems.

Full text: PDF file (241 kB)
References: PDF file   HTML file

English version:
Siberian Advances in Mathematics, 2012, 22:3, 192–203

Bibliographic databases:

Document Type: Article
UDC: 514.752.22+517
Received: 31.05.2010

Citation: Yu. G. Nikonorov, “Asymptotics of tangent points for planar curves”, Mat. Tr., 14:1 (2011), 141–157; Siberian Adv. Math., 22:3 (2012), 192–203

Citation in format AMSBIB
\Bibitem{Nik11}
\by Yu.~G.~Nikonorov
\paper Asymptotics of tangent points for planar curves
\jour Mat. Tr.
\yr 2011
\vol 14
\issue 1
\pages 141--157
\mathnet{http://mi.mathnet.ru/mt210}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2858661}
\transl
\jour Siberian Adv. Math.
\yr 2012
\vol 22
\issue 3
\pages 192--203
\crossref{https://doi.org/10.3103/S1055134412030030}


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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. Nikonorov Yu.G., “Asymptotic Behavior of Support Points for Planar Curves”, J. Math. Anal. Appl., 391:1 (2012), 147–158  crossref  mathscinet  zmath  isi  elib  scopus
    2. Yu. G. Nikonorov, “Asymptotics of mean value points in the Schwarz theorem for divided differences”, Siberian Adv. Math., 25:1 (2015), 56–75  mathnet  crossref  mathscinet
    3. 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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