Approximation by Kantorovich-Szasz Type Operators Based on Brenke Type Polynomials

ATAKUT Ç., BÜYÜKYAZICI İ.

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, vol.37, no.12, pp.1488-1502, 2016 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 37 Issue: 12
  • Publication Date: 2016
  • Doi Number: 10.1080/01630563.2016.1216447
  • Journal Name: NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1488-1502
  • Keywords: Brenke polynomials, Kantorovich-Szasz type operators, modulus of smoothness, Peetre K-functional, rate of convergence, weighted space
  • Ankara University Affiliated: Yes

Abstract

In this article, we give a generalization of the Kantorovich-Szasz type operators defined by means of the Brenke type polynomials introduced in the literature and obtain convergence properties of these operators by using Korovkin's theorem. Some graphical examples using the Maple program for this approximation are given. We also establish the order of convergence by using modulus of smoothness and Peetre's K-functional and give a Voronoskaja type theorem. In addition, we deal with the convergence of these operators in a weighted space.