The Bézier variant of Kantorovich type λ-Bernstein operators

Abstract

Abstract In this paper, we introduce the Bézier variant of Kantorovich type λ-Bernstein operators with parameter λ∈[−1,1] $\lambda\in[-1,1]$. We establish a global approximation theorem in terms of second order modulus of continuity and a direct approximation theorem by means of the Ditzian–Totik modulus of smoothness. Finally, we combine the Bojanic–Cheng decomposition method with some analysis techniques to derive an asymptotic estimate on the rate of convergence for some absolutely continuous functions.

Keywords

• λ-Bernstein operators
• Basis functions
• Modulus of continuity
• Rate of convergence
• Absolutely continuous functions