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Positivity

, Volume 19, Issue 2, pp 237–249 | Cite as

Power series of the operators \(U_n^{\varrho }\)

  • Heiner Gonska
  • Ioan Raşa
  • Elena Dorina Stănilă
Article

Abstract

We study power series of members of a class of positive linear operators reproducing linear function constituting a link between genuine Bernstein-Durrmeyer and classical Bernstein operators. Using the eigenstructure of the operators we give a non-quantitative convergence result towards the inverse Voronovskaya operators. We include a quantitative statement via a smoothing approach.

Keywords

Power series Geometric series Positive linear operator Bernstein-type operator Genuine Bernstein-Durrmeyer operator Degree of approximation Eigenstructure Moduli of continuity 

Mathematics Subject Classification (2000)

41A10 41A17 41A25 41A36 

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Copyright information

© Springer Basel 2014

Authors and Affiliations

  • Heiner Gonska
    • 1
  • Ioan Raşa
    • 2
  • Elena Dorina Stănilă
    • 1
  1. 1.Faculty of MathematicsUniversity of Duisburg-EssenDuisburgGermany
  2. 2.Department of MathematicsTechnical University of Cluj-NapocaCluj-NapocaRomania

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