2017
Том 69
№ 9

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

Gonska H., Păltănea R.

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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.

English version (Springer): Ukrainian Mathematical Journal 62 (2010), no. 7, pp 1061-1072.

Citation Example: Gonska H., Păltănea R. Quantitative convergence theorems for a class of Bernstein–Durrmeyer operators preserving linear functions // Ukr. Mat. Zh. - 2010. - 62, № 7. - pp. 913–922.

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