Integral-type generalizations of operators obtained from certain multivariate polynomials


Erkus-Duman E. , DUMAN O.

CALCOLO, vol.45, no.1, pp.53-67, 2008 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 45 Issue: 1
  • Publication Date: 2008
  • Doi Number: 10.1007/s10092-008-0143-6
  • Title of Journal : CALCOLO
  • Page Numbers: pp.53-67

Abstract

In this work, we mainly focus on the Kantorovich-type (integral-type) generalizations of the positive linear operators obtained from the Chan-Chyan-Srivastava multivariable polynomials. Using the notion of A-statistical convergence, we obtain various approximation theorems including a statistical Korovkin-type result and rates of A-statistical convergence with the help of the modulus of continuity, Lipschitz class functionals and Peetre's K-functionals. We also introduce an sth order generalization of our approximating operators.