Bézier variant of genuine-Durrmeyer type operators based on Pólya distribution


Neer, Trapti, Acu, Ana Maria and Agrawal, P. N.


Abstract

carpathian_33_1_073_086_abstract

In this paper we introduce the Bézier variant of genuine-Durrmeyer type operators having Pólya basis functions. We give a global approximation theorem in terms of second order modulus of continuity, a\linebreak direct approximation theorem by means of the Ditzian-Totik modulus of smoothness and a Voronovskaja type theorem by using the Ditzian-Totik modulus of smoothness. The rate of convergence for functions whose derivatives are of bounded variation is obtained. Further, we show the rate of convergence of these operators to certain functions by illustrative graphics using the Maple algorithms.

Additional Information

Author(s)

Acu, Ana Maria, Agrawal, P. N., Neer, Trapti