ASYMPTOTIC APPROXIMATION BYBERNSTEIN-DURRMEYER OPERATORS AND THEIR DERIVATIVES |
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Authors: | Abel Ulrich |
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Affiliation: | (1) Fachhochschule Giessen-Friedberg, University of Applied Sciences Fachbereich MND, Wilhelm-Leuschner-Strasse 13, D-61169 Friedberg, Germany |
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Abstract: | The concern of this paper is to study local approximation properties of the Bernstein-Durrmeyer operators Mn. We derive the complete asymptotic expansion of the operators Mn and their derivatives as n tends to infinity. It turns out that the appropriate representation is a series of reciprocal factorials. All coefficients are calculated explicitly in a very concise form. Our main theorem contains several earlier partial results as special cases. Finally, we obtain a Voronovskaja-type formula for simultaneous approximation by linear combinations of Mn, |
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