Abdullah Rashid Alotaibi

In this article, we construct a new class of summation-integral type positive operators linked with Frobenius-Euler polynomials. We obtain local approximation, Voronovskaya type theorems and rate of convergence of these operators within a weighted function space. Also, the rate of convergence for functions with derivatives of bounded variation is established. Finally, we examine the convergence rates of the operators through graphical representations.

This work introduces -Bézier–Bernstein-integral type operators, along with local approximation results, a direct approximation theorem that leverages the Ditzian–Totik modulus of smoothness, and a quantitative Voronovskaja-type theorem using the Ditzian–Totik modulus of continuity. Additionally, we derive the convergence rate for differential functions with bounded variation in their derivatives.