Generalized Szász–Mirakyan operators involving Brenke type polynomials

Abstract

The aim of the present paper is to introduce generalized Szász–Mirakyan operators including Brenke type polynomials and investigate their approximation properties. 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. We also give asymptotic formula and the convergence of the derivatives for these operators. Furthermore, an example of Szász–Mirakyan operators including Gould–Hopper polynomials is presented. In the end, we show graphical representation.