Ukrainian Mathematical Journal

, Volume 62, Issue 7, pp 1061–1072 | Cite as

Quantitative convergence theorems for a class of Bernstein–Durrmeyer operators preserving linear functions

  • H. Gonska
  • R. Păltănea

We supplement recent results on a class of Bernstein–Durrmeyer operators preserving linear functions. This is done by discussing two limiting cases and proving quantitative Voronovskaya-type assertions involving the first-order and second-order moduli of smoothness. The results generalize and improve earlier statements for Bernstein and genuine Bernstein–Durrmeyer operators.


Uniform Convergence Bernstein Polynomial Positive Linear Operator Bernstein Operator Durrmeyer Operator 
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Copyright information

© Springer Science+Business Media, Inc. 2010

Authors and Affiliations

  • H. Gonska
    • 1
  • R. Păltănea
    • 2
  1. 1.University of Duisburg-EssenEssenGermany
  2. 2.Transilvania UniversityBraşovRomania

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