In this paper we consider a new definition of generalized sampling type series using an approach introduced by Durrmeyer for Bernstein polynomials. We establish an asymptotic formula for functions with a polynomial growth and as a consequence we obtain a Voronovskaja type formula. Then we consider suitable linear combinations that provide a better order of approximation. Finally particular examples are given, in particular certain central B-splines are discussed
Asymptotic expansion of generalized Durrmeyer sampling type series
BARDARO, Carlo;MANTELLINI, Ilaria
2014
Abstract
In this paper we consider a new definition of generalized sampling type series using an approach introduced by Durrmeyer for Bernstein polynomials. We establish an asymptotic formula for functions with a polynomial growth and as a consequence we obtain a Voronovskaja type formula. Then we consider suitable linear combinations that provide a better order of approximation. Finally particular examples are given, in particular certain central B-splines are discussedFile in questo prodotto:
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