Generalization of Szasz operators involving Brenke type polynomials

Abstract

The purpose of this paper is to give a generalization of Szasz operators defined by means of the Brenke type polynomials. We obtain convergence properties of our operators with the help of Korovkin’s theorem and the order of convergence by using a classical approach, the second modulus of continuity and Peetre’s K-functional. An explicit example with our operators including Gould–Hopper polynomials which generalize Szasz operators in a natural way is given.