Approximation by Stancu-Durrmeyer type operators based on P\'{o}lya-Eggenberger distribution

Abstract

In the present paper we introduce the Durrmeyer type modification of Stancu operators based on P\'{o}lya-Eggenberger distribution. For these new operators some indispensable auxiliary results are established in the second section. Our further study focuses on a Voronovskaja type asymptotic formula and some estimates of the rate of approximation involving modulus of smoothness, respectively Ditzian-Totik modulus of smoothness. The rate of convergence for differential functions whose derivatives are of bounded variation is also obtained.