The approximation of bivariate Chlodowsky-Szász-Kantorovich-Charlier-type operators

Abstract

Abstract In this paper, we introduce a bivariate Kantorovich variant of combination of Szász and Chlodowsky operators based on Charlier polynomials. Then, we study local approximation properties for these operators. Also, we estimate the approximation order in terms of Peetre’s K-functional and partial moduli of continuity. Furthermore, we introduce the associated GBS-case (Generalized Boolean Sum) of these operators and study the degree of approximation by means of the Lipschitz class of Bögel continuous functions. Finally, we present some graphical examples to illustrate the rate of convergence of the operators under consideration.

Keywords

• GBS operators
• Chlodowsky and Szász-type operators
• Charlier polynomials
• partial moduli of continuity
• modulus of smoothness
• degree of approximation