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 discussed
2014
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11391/1167274
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