On the Approximations and Symmetric Properties of Frobenius–Euler–Şimşek Polynomials Connecting Szász Operators

This study focuses on approximating continuous functions using Frobenius–Euler–Simsek polynomial analogues of Szász operators. Test functions and central moments are computed to study convergence uniformly, approximation order by these operators. Next, we investigate approximation order uniform convergence via Korovkin result and the modulus of smoothness for functions in continuous functional spaces. A Voronovskaja theorem is also explored approximating functions which belongs to the class of function having first and second order continuous derivative. Further, we discuss numerical error and graphical analysis. In the last, two dimensional operators are constructed to discuss approximation for the class of two variable continuous functions.