A New Generalization of Sz´asz Operators

Year 2025, Issue: 52, 61 - 71, 30.09.2025

Harun Çiçek , Naıruz Ousman , Aydın İzgi

https://doi.org/10.53570/jnt.1753639

Abstract

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 $q$.

Keywords

Korovkin theorem , linear positive operators , Lipschitz conditions , rate of approximation , Voronovskaja-type approximation

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