Jakimovski–Leviatan operators of Durrmeyer type involving Appell polynomials

Abstract

The purpose of the present paper is to establish the rate of convergence for a Lipschitz-type space andobtain the degree of approximation in terms of Lipschitz-type maximal function for the Durrmeyer type modification ofJakimovski–Leviatan operators based on Appell polynomials. We also study the rate of approximation of these operatorsin a weighted space of polynomial growth and for functions having a derivative of bounded variation.