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On Genuine Bernstein–Durrmeyer Operators |
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| Authors: | Heiner Gonska Daniela Kacsó Ioan Ra?a |
| Institution: | 1. Department of Mathematics, University of Duisburg-Essen, Forsthausweg 2, D-47048, Duisburg, Germany 2. Department of Mathematics, University of Bochum, Universit?tsstr. 150, D-44780, Bochum, Germany 3. Department of Mathematics, Technical University, Str. C. Daicoviciu 15, RO-400020, Cluj-Napoca, Romania |
| 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. Received: January 26, 2007. |
| Keywords: | 41A36 41A25 41A17 41A10 20Mxx 47A75 |
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