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

Md. Nasiruzzaman () and Abdullah Alotaibi ()
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Md. Nasiruzzaman: Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk 47191, Saudi Arabia
Abdullah Alotaibi: Operator Theory and Applications Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia

Mathematics, 2025, vol. 13, issue 23, 1-22

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.

Keywords: Kantorovich operators; Schurer operators; quantum calculus; global approximation; Voronovskaja-type theorem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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