Abstract.
We continue the studies on the so–called genuine Bernstein–Durrmeyer operators U n by establishing a recurrence formula for the moments and by investigating the semigroup T(t) approximated by U n . Moreover, for sufficiently smooth functions the degree of this convergence is estimated. We also determine the eigenstructure of U n , compute the moments of T(t) and establish asymptotic formulas.
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Dedicated to Academician Dimitrie D. Stancu on the occasion of his 80th birthday
Received: January 26, 2007.
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Gonska, H., Kacsó, D. & Raşa, I. On Genuine Bernstein–Durrmeyer Operators. Result. Math. 50, 213–225 (2007). https://doi.org/10.1007/s00025-007-0242-8
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DOI: https://doi.org/10.1007/s00025-007-0242-8