A New Generalization of Sz´asz Operators

The purpose of this study is to define a new generalization of Sz\'{a}sz operators. The paper proceeds to study the rate of convergence and approximation properties of the newly defined Sz\'{a}sz operator on closed subintervals of the real axis. Subsequently, it investigates the Voronovskaja-type approximation and the local approximation of the new Sz\'{a}sz operator using functions satisfying the Lipschitz condition. Additionally, this paper analyzes the rate of convergence for $\digamma$ and $\digamma^\prime$ using the continuity modulus. Finally, it graphically illustrates the approximation of the new generalization of the Sz\'{a}sz operator to a continuous function with a numerical example and provides a numerical table of error values in the approximation of a continuous function for different values of $n$ and $q$.