Grüss and Grüss-Voronovskaya-type estimates for some Bernstein-type polynomials of real and complex variables

• Sorin G. Gal ^[1] ; Heiner Gonska ^[2]
  1. [1] University of Oradea

     University of Oradea

     Rumanía

     
  2. [2] University of Duisburg-Essen

     University of Duisburg-Essen

     Kreisfreie Stadt Essen, Alemania

     
• Localización: Jaen journal on approximation, ISSN 1889-3066, ISSN-e 1989-7251, Vol. 7, Nº. 1, 2015, págs. 97-122
• Idioma: inglés
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• Resumen

  • The first aim of this paper is to prove a Grüss-Voronovskaya estimate for Bernstein and for a class of Bernstein-Durrmeyer polynomials on [0, 1]. Then, Grüss and Grüss-Voronovskaya estimates for their corresponding operators of complex variable on compact disks are obtained. Finally, the results are extended to Bernstein-Faber polynomials attached to compact sets in the complex plane.