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
Gonska, H., and R. Păltănea. “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