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

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

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

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

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    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)
  • János PINTZ (Rényi Institute of Mathematics)
  • Ferenc SCHIPP (Eötvös University Budapest and University of Pécs)
  • Sándor SZABÓ (University of Pécs)

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  • Ferenc HARTUNG (University of Pannonia, Veszprém)
  • Ferenc WEISZ (Eötvös University, Budapest)

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  • István BERKES (Rényi Institute of Mathematics)
  • Károly BEZDEK (University of Calgary)
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  • 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)

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