An identity for a general class of approximation operators

  • Authors:

  • Ulrich Abel

  • Affiliations:

  • Fachbereich MND, Fachhochschule Giessen-Friedberg, University of Applied Sciences, Friedberg, Germany

  • Venue:
  • Journal of Approximation Theory
  • Year:
  • 2006

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Abstract

We prove an identity for basis functions of a general family of positive linear operators. It covers as special cases the Bernstein, Szász-Mirakjan and Baskakov operators. A corollary of our result can be considered a pointwise orthogonality relation. The Bernstein case is the univariate case of a remarkable identity which recently was presented by Jetter and Stöckler. As an application we give a representation of a restricted dual basis and define a class of quasi-interpolants.