Author:
Tatiana M. Nikiforova N. 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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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.

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    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).

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  • [2]

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

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  • [3]

    Bernstein, S. N. Sur la limitation des dérivées des polynômes. C. R. Acad. Sc. Paris 190 (1930), 338340.

  • [4]

    De Bruijn, N. G. Inequalities concerning polynomials in the complex domain. Nederl. Akad. Wetensch. Proc. 50 (1947), 12651272.

  • [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), 289297.

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  • [6]

    Riesz, M. Eine trigonometrische Interpolationsformel und einige Ungleichungen für Polynome. Bull. Amer. Math. Soc. 44, 4 (1938), 289297.

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  • [7]

    Sewell, W. E. On the polynomial derivative constant for an ellipse. Amer. Math. Monthly. 44 (1937), 895903.

  • [8]

    Szego, G. Bemerkungen zu einem Satz von J. H. Grace über die Wurzeln algebraischer Gleichungen. Math. Z. 13 (1922), 2855.

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Editor in Chief: László TÓTH (University of Pécs)

Honorary Editors in Chief:

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

Deputy Editors in Chief:

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

Editorial Board

  • Attila BÉRCZES (University of Debrecen, Debrecen, Hungary)
  • István BERKES (Rényi Institute of Mathematics, Budapest, Hungary)
  • Károly BEZDEK (University of Calgary, Calgary, Canada)
  • György DÓSA (University of Pannonia, Veszprém, Hungary)
  • Balázs KIRÁLY – Managing Editor (University of Pécs, Pécs, Hungary)
  • Vedran KRCADINAC (University of Zagreb, Zagreb, Croatia) 
  • Željka MILIN ŠIPUŠ (University of Zagreb, Zagreb, Croatia)
  • Gábor NYUL (University of Debrecen, Debrecen, Hungary)
  • Margit PAP (University of Pécs, Pécs, Hungary)
  • István PINK (University of Debrecen, Debrecen, Hungary)
  • Mihály PITUK (University of Pannonia, Veszprém, Hungary)
  • Jörg THUSWALDNER (Montanuniversität Leoben, Leoben, Austria)
  • Zsolt TUZA (University of Pannonia, Veszprém, Hungary)

Advisory Board

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

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

  • Mathematical Reviews
  • Zentralblatt
  • DOAJ

Publication Model Gold Open Access
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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)