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

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 Grüss-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.

Keywords:

• Bernstein-Kantorovich operator
• Lipschitz continuous functions
• modulus of continuity
• rate of convergence
• Stancu operators
• Voronovskaja asymptotic formula

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• Primary 41A10
• 41A25
• 41A36
• Secondary 26A16
• 40C05

Acknowledgments

We thank the Editors and the anonymous reviewer for his/her helpful suggestions, which improved this paper significantly.