Quantitative convergence theorems for a class of Bernstein–Durrmeyer operators preserving linear functions
- 106 Downloads
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.
KeywordsUniform Convergence Bernstein Polynomial Positive Linear Operator Bernstein Operator Durrmeyer Operator
Unable to display preview. Download preview PDF.
- 1.H. Gonska and R. Păltănea, “Simultaneous approximation by a class of Bernstein–Durrmeyer operators preserving linear functions,” Czech. Math. J. (to appear).Google Scholar
- 3.H. Gonska, Quantitative Aussagen zur Approximation durch positive lineare Operatoren, Doctoral-Degree Thesis, University of Duisburg (1979).Google Scholar
- 5.H. Gonska and I. Raşa, “A Voronovskaya estimate with second-order modulus of smoothness,” Proc. Math. Inequal. (Sibiu / Romania, Sept. 2008) (to appear).Google Scholar
- 6.H. Gonska and I. Raşa, Four Notes on Voronovskaya’s Theorem, Schriftenr. Fachbereichs Math. Univ. Duisburg-Essen (2009).Google Scholar