Approximation by Jakimovski-Leviatan-Pǎltǎnea operators involving Sheffer polynomials

Abstract

The aim of the present paper is to introduce Jakimovski-Leviatan-Pǎltǎnea operators which involve Sheffer polynomials. We investigate approximation properties of our operators with the help of the universal Korovkin-type property and also establish the rate of convergence by using the modulus of continuity, second order modulus of smoothness and Petree’s K-functional. Furthermore, we study the approximation by functions of bounded variations. Some graphical examples of the convergence of our operators and error estimation are also given.