Blending type approximation by Bernstein-Durrmeyer type operators

Abstract

In this note, we introduce the Durrmeyer variant of Stancuoperators that preserve the constant functions depending onnon-negative parameters. We give a global approximation theorem interms of the Ditzian-Totik modulus of smoothness, a Voronovskajatype theorem and a local approximation theorem by means of secondorder modulus of continuity. Also, we obtain the rate ofapproximation for absolutely continuous functions having aderivative equivalent with a function of bounded variation.Lastly, we compare the rate of approximation of theStancu-Durrmeyer operators and genuine Bernstein-Durrmeyeroperators to certain function by illustrative graphics with thehelp of the Mathematica software.