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.
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 62, No. 7, pp. 913–922, July, 2010.
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Gonska, H., Păltănea, R. Quantitative convergence theorems for a class of Bernstein–Durrmeyer operators preserving linear functions. Ukr Math J 62, 1061–1072 (2010). https://doi.org/10.1007/s11253-010-0413-8
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DOI: https://doi.org/10.1007/s11253-010-0413-8