Convergence by Class of Kantorovich-Type q -Szász Operators and Comprehensive Results

Md. Nasiruzzaman, Mohammad Farid () and Nadeem Rao
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Md. Nasiruzzaman: Department of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 4279, Tabuk 71491, Saudi Arabia
Mohammad Farid: Department of Mathematics, College of Science, Qassim University, Saudi Arabia
Nadeem Rao: Department of Mathematics, University Center for Research and Development, Chandigarh University, Mohali 140413, Punjab, India

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

Abstract: In this paper, we primarily use Stancu variants of Kantorovich-type operators to investigate the convergence and other associated properties of new Szász–Mirakjan operators. We compute the moments and central moments of the new Szász–Mirakjan operators by q -integers and propose their modified Kantorovich form. More specifically, we examine the convergence characteristics in the space of continuous functions. With the use of the modulus of continuity and the integral modulus of continuity, we determine the degree of convergence. Additionally, we obtain the Voronovskaja type theorems. To validate convergence, we conclude with a numerical example and graphical illustration of the operator sequences.

Keywords: Szász–Mirakjan operators; q-integrals; Korovkin’s theorem; modulus of continuity; Peetre’s K-functional; approximation algorithms; Voronovskaja-type theorem; mathematical operators (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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