On Kantorovich process of a sequence of the generalized linear positive operators


İSPİR N., ARAL A., Dogru O.

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, vol.29, pp.574-589, 2008 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 29
  • Publication Date: 2008
  • Doi Number: 10.1080/01630560802099365
  • Journal Name: NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.574-589
  • Keywords: bounded variation, derivatives of bounded variation, Kantorovich-type operators, linear positive operators, rate of convergence, total variation, weighted approximation, CONVERGENCE, POLYNOMIALS, DERIVATIVES
  • Gazi University Affiliated: Yes

Abstract

We define the Kantorovich variant of the generalized linear positive operators introduced by Ibragimov and Gadjiev in 1970. We investigate direct approximation result for these operators on p-weighted integrable function spaces and also estimate their rate of convergence for absolutely continuous functions having a derivative coinciding a.e., with a function of bounded variation.