Kantorovich Extension of Parametric Generalized q-Schurer Operators and Their Approximation Properties

Source abstract

This paper aims to extend, within the context of quantum calculus, the α-Bernstein–Schurer operators (α∈[0,1]) to Kantorovich form. Using the Ditzian–Totik modulus of continuity and the Lipschitz-kind maximal function for our recently extended operators, we first examine the Korovkin-type theorem before studying the global approximation and rate of convergence, respectively. Furthermore, Taylor’s formula is used to present Voronovskaja-type theorems. Lastly, the aforementioned operators are validated through the numerical results with graphical representation.