Geometric series of positive linear operators and the inverse Voronovskaya theorem on a compact interval

We define the associated geometric series for a large class of positive linear operators and study the convergence of the series in the case of sequences of admissible operators. We obtain an inverse Voronovskaya theorem and we apply our results to the Bernstein operators and a class of Bernstein–Du...

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Veröffentlicht in:	Journal of approximation theory Jg. 184; S. 163 - 175
Hauptverfasser:	Abel, Ulrich, Ivan, Mircea, Păltănea, Radu
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	Elsevier Inc 01.08.2014
Schlagworte:	Bernstein operators Bernstein–Durrmeyer type operators Inverse Voronovskaya theorem Positive linear operators Series of operators Bernstein operators 41A35 41A36 Inverse Voronovskaya theorem Series of operators Positive linear operators 41A27 Bernstein–Durrmeyer type operators
ISSN:	0021-9045, 1096-0430
Online-Zugang:	Volltext
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Zusammenfassung:	We define the associated geometric series for a large class of positive linear operators and study the convergence of the series in the case of sequences of admissible operators. We obtain an inverse Voronovskaya theorem and we apply our results to the Bernstein operators and a class of Bernstein–Durrmeyer type operators.
ISSN:	0021-9045 1096-0430
DOI:	10.1016/j.jat.2014.05.011