Generalized Bernstein–Durrmeyer operators of blending type

Abstract

In this note, we derive some approximation properties of the generalized Bernstein-Kantorovich-type operators based on two nonnegative parameters consid- ered by A. Kajla [Appl. Math. Comput. 2018]. We establish a Voronovskaja-type asymptotic theorem for these operators. The rate of convergence for differential func- tions whose derivatives are of bounded variation is also derived. Finally, we show the convergence of the operators to certain functions by illustrative graphics using Mathe- matica software.