Abstract

In this note, we introduce the Durrmeyer variant of Stancu operators that preserve the constant functions depending on non-negative parameters. We give a global approximation theorem in terms of the Ditzian-Totik modulus of smoothness, a Voronovskaja type theorem and a local approximation theorem by means of second order modulus of continuity. Also, we obtain the rate of approximation for absolutely continuous functions having a derivative equivalent with a function of bounded variation. Lastly, we compare the rate of approximation of the Stancu-Durrmeyer operators and genuine Bernstein-Durrmeyer operators to certain function by illustrative graphics with the help of the Mathematica software.

Keywords: Stancu operators; global approximation; rate of convergence; \mbox{modulus} of continuity; Steklov mean.

MSC: 41A25, 26A15

Pages:  40$-$54     

Volume  70 ,  Issue  1 ,  2018