Asymptotic expansion of generalized Durrmeyer sampling type series

• Carlo Bardaro ^[1] ; Ilaria Mantellini ^[1]
  1. [1] Università di Perugia

     Università di Perugia

     Perusa, Italia

     
• Localización: Jaen journal on approximation, ISSN 1889-3066, ISSN-e 1989-7251, Vol. 6, Nº. 2, 2014, págs. 143-165
• Idioma: inglés
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• Resumen

  • In this paper we consider a new definition of generalized sampling type series using an approach introduced by Durrmeyer for the Bernstein polynomials. We establish an asymptotic formula for functions f 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, some examples are given, in particular certain central B-splines are discussed.