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

  • H. Gonska Univ. Duisburg-Essen, Germany
  • R. Păltănea

Abstract

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.
Published
25.07.2010
How to Cite
GonskaH., and PăltăneaR. “Quantitative Convergence Theorems for a Class of Bernstein–Durrmeyer Operators Preserving Linear Functions”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 62, no. 7, July 2010, pp. 913–922, https://umj.imath.kiev.ua/index.php/umj/article/view/2924.
Section
Research articles