The Bézier variant of Kantorovich type λ-Bernstein operators.

In this paper, we introduce the Bézier variant of Kantorovich type λ-Bernstein operators with parameter [Formula: see text]. 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.