On the approximation of Kantorovich-type Szàsz-Charlier operators

Abstract In this study, we introduce the Kantorovich-type modified Szàsz-Charlier operators and examine their approximation properties within the framework of fractional modeling and control theory. These operators are defined using the Korovkin-type theorem, and their local approximation properties are analyzed in detail. Additionally, the approximation rate of these operators is estimated using the modulus of continuity and functions in the Lipschitz class. To gain a deeper understanding of their approximation capabilities, we calculate their central moments. Furthermore, the convergence rates are determined based on the modulus of continuity, and a Voronovskaja-type asymptotic formula is provided for these operators. Our study also investigates the approximation speed in weighted spaces, which is crucial for addressing complex dynamical systems in science and engineering. The approximation speed in weighted spaces is evaluated using the weighted modulus of continuity and the Peetre- K function. Finally, illustrative graphics generated using Maple are presented to visualize the convergence of operators to specific functions.