Approximation Properties of a Certain Modification of  Durrmeyer Operators

Abstract

We study approximation properties of a new operator DM,1 n (f, x) introduced by Acu et al. in [Results Math 74:90, (2019)] for Lebesgue integrable functions in [0,1]. An error estimate by the Bezier variant of the operators DM,1 n (f, x)is also obtained for the functions of bounded variation. By relevant numerical examples, the orders of approximation by the operator DM,1 n (f, x) and the modified-Bernstein-Durrmeyer operator are also compared.