Mathematica Pannonica
Volume/Issue:
Volume 27_NS1: Issue 2
Inequalities for the First and Second Derivatives of Algebraic Polynomials on an Ellipse
Author:
Tatiana M. NikiforovaN. N. Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences 16 S. Kovalevskaya Str., Yekaterinburg, Russia
Ural Federal University 19 Mira Str., Yekaterinburg, Russia

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Pages:
233–240
Online Publication Date:
08 Nov 2021
Publication Date:
18 Nov 2021
Article Category:
Research Article
DOI:
https://doi.org/10.1556/314.2021.00020
Keywords:
Polynomial; derivative; ellipse; majorant; Bernstein inequality; Duffin–Schaeffer inequality; Vidensky inequality
Open access

We prove a theorem on the preservation of inequalities between functions of a special form after differentiation on an ellipse. In particular, we obtain generalizations of the Duffin–Schaeffer inequality and the Vidensky inequality for the first and second derivatives of algebraic polynomials to an ellipse.

  • [1]

    Bernstein, S. N. Sur l’ordre de la meilleure approximation des fonctions continues par des polynômes de degré donné. Mémoires de l’Académie royale de Belgique 4, 2 (1912).

    • Search Google Scholar
    • Export Citation
  • [2]

    Bernstein, S. N. Leçons sur les Propriétés Extrémales et la Meilleure Approximation des Fonctions Analytiques d’une Variable Réelle. Paris, 1926.

    • Search Google Scholar
    • Export Citation
  • [3]

    Bernstein, S. N. Sur la limitation des dérivées des polynômes. C. R. Acad. Sc. Paris 190 (1930), 338–340.

  • [4]

    De Bruijn, N. G. Inequalities concerning polynomials in the complex domain. Nederl. Akad. Wetensch. Proc. 50 (1947), 1265–1272.

  • [5]

    Duffin, R. J., and Schaeffer, A. C. On some inequalities of S. Bernstein and W. Marko_ for derivatives of polynomials. Bull. Amer. Math. Soc. 44, 4 (1938), 289–297.

    • Search Google Scholar
    • Export Citation
  • [6]

    Riesz, M. Eine trigonometrische Interpolationsformel und einige Ungleichungen für Polynome. Bull. Amer. Math. Soc. 44, 4 (1938), 289–297.

    • Search Google Scholar
    • Export Citation
  • [7]

    Sewell, W. E. On the polynomial derivative constant for an ellipse. Amer. Math. Monthly. 44 (1937), 895–903.

  • [8]

    Szego, G. Bemerkungen zu einem Satz von J. H. Grace über die Wurzeln algebraischer Gleichungen. Math. Z. 13 (1922), 28–55.

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Cover Mathematica Pannonica
Mathematica Pannonica
Print ISSN:
0865-2090
Online ISSN:
2786-0752
The Instruction for Authors is available in PDF format. Please, download the file from HERE.
Please, download the LaTeX template from HERE.

Editor in Chief: László TÓTH (University of Pécs)

Honorary Editors in Chief:

  • † István GYŐRI (University of Pannonia, Veszprém)
  • János PINTZ (Rényi Institute of Mathematics)
  • Ferenc SCHIPP (Eötvös University Budapest and University of Pécs)
  • Sándor SZABÓ (University of Pécs)
     

Deputy Editors in Chief:

  • Erhard AICHINGER (JKU Linz)
  • Ferenc HARTUNG (University of Pannonia, Veszprém)
  • Ferenc WEISZ (Eötvös University, Budapest)

Editorial Board

  • György DÓSA (University of Pannonia, Veszprém)
  • István BERKES (Rényi Institute of Mathematics)
  • Károly BEZDEK (University of Calgary)
  • Balázs KIRÁLY – Managing Editor (University of Pécs)
  • Vedran KRCADINAC (University of Zagreb) 
  • Željka MILIN ŠIPUŠ (University of Zagreb)
  • Margit PAP (University of Pécs)
  • Mihály PITUK (University of Pannonia, Veszprém)
  • Jörg THUSWALDNER (Montanuniversität Leoben)
  • Zsolt TUZA (University of Pannonia, Veszprém)

Advisory Board

  • Szilárd RÉVÉSZ (Rényi Institute of Mathematics)  - Chair
  • Gabriella BÖHM (Akadémiai Kiadó, Budapest)
  • György GÁT (University of Debrecen)

University of Pécs,
Faculty of Sciences,
Institute of Mathematics and Informatics
Department of Mathematics
7624 Pécs, Ifjúság útja 6., HUNGARY
(36) 72-503-600 / 4179
ltoth@gamma.ttk.pte.hu

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Mathematica Pannonica
Language English
Size A4
Year of
Foundation		 1990
Volumes
per Year		 1
Issues
per Year		 2
Founder Akadémiai Kiadó
Founder's
Address		 H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
Publisher Akadémiai Kiadó
Publisher's
Address		 H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
Responsible
Publisher		 Chief Executive Officer, Akadémiai Kiadó
ISSN 2786-0752 (Online)
ISSN 0865-2090 (Print)

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