TY  - JOUR
T1  - A New Generalization of Sz´asz Operators
AU  - Çiçek, Harun
AU  - Ousman, Naıruz
AU  - İzgi, Aydın
PY  - 2025
DA  - September
Y2  - 2025
DO  - 10.53570/jnt.1753639
JF  - Journal of New Theory
JO  - JNT
PB  - Naim ÇAĞMAN
WT  - DergiPark
SN  - 2149-1402
SP  - 61
EP  - 71
IS  - 52
LA  - en
AB  - 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 $q$.
KW  - Korovkin theorem
KW  - linear positive operators
KW  - Lipschitz conditions
KW  - rate of approximation
KW  - Voronovskaja-type approximation
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UR  - https://doi.org/10.53570/jnt.1753639
L1  - https://dergipark.org.tr/en/download/article-file/5102523
ER  -