{Generalization of Sz\'asz-Baskakov Operators Based on Touchard Polynomials

Abstract

In this study, we present a generalization of the Sz\'asz-Baskakov operators using Touchard polynomials. First, we establish the rate of convergence for the newly defined operators. Subsequently, several approximation results are established. Finally, Voronovskaya-type theorem is proved and some graphical results are given to show the rate of convergence of constructed operators to a given function $f$.