A Genuine Family of Bernstein-Durrmeyer Type Operators Based on Polya Basis Functions

Abstract

In this paper, we construct a genuine family of Bernstein-Durrmeyer type operators based on Polya basis functions. We establish some moment estimates and the direct results which include global approximation theorem in terms of classical modulus of continuity, local approximation theorem in terms of the second order Ditizian-Totik modulus of smoothness, Voronovskaya-type asymptotic theorem
and a quantitative estimate of the same type. Lastly, we study the approximation of functions having a derivative of bounded variation.