Extended Bernstein-Kantorovich-Stancu Operators with Multiple Parameters and Approximation Properties


Kadak U., Ozluk M.

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 2021 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume:
  • Publication Date: 2021
  • Doi Number: 10.1080/01630563.2021.1895833
  • Title of Journal : NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION

Abstract

In this paper, we introduce a novel extension of the Bernstein-Kantorovich-Stancu type operator of degree n with the help of multiple shape parameters. Voronovskaja and Gruss-Voronovskaja type approximation theorems are examined via Ditzian-Totik moduli of smoothness. We investigate basic statistical convergence properties with respect to a non-negative regular summability matrix. Moreover, using Ditzian-Totik moduli, local and global approximation properties associated to the proposed operator have been established. Finally, several illustrative examples are presented to demonstrate the efficiency, applicability and validity of the operator. The graphical and numerical results verify that the proposed operator gives better approximation as well as expand the previous Bernstein-Kantorovich type modifications including single parameter.