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Journals / Turkish Journal of Mathematics and Computer Science / 2026 / Volume: 18 Issue: 3

A New Generalized $q$-Szasz-Mirakyan-Kantorovich Operators

Harun Çiçek(BITLIS EREN UNIVERSITY)0000-0003-3018-3015
Betül Öztel(ISTANBUL ESENYURT UNIVERSITY)0000-0002-5973-9323
Aydın İzgi(HARRAN UNIVERSITY)0000-0003-3715-8621
Pages
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Publication Date
2026-10-13
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AI Summary & Key Takeaways

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⚡ TL;DR(Too Long; Didn't Read)

Subsequently, a novel generalized $q$-Szasz-Mirakyan-Kantorovich operator on $q$-integers is constructed, and the classical and statistical approximation properties of this new q-operator are studied.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In the present study, a novel generalization of the Szasz-Mirakyan-Kantorovich operators is delineated.
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Key Findings & Data:Utilising the continuity modulus and functions satisfying the Lipschitz condition, the rate of approximation of the operator is calculated.
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Conclusion & Impact:Subsequently, a novel generalized $q$-Szasz-Mirakyan-Kantorovich operator on $q$-integers is constructed, and the classical and statistical approximation properties of this new q-operator are studied.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Approximation theory · linear positive operators · q-analysis

Abstract

In the present study, a novel generalization of the Szasz-Mirakyan-Kantorovich operators is delineated. The approximation properties of the aforementioned operator are investigated. Utilising the continuity modulus and functions satisfying the Lipschitz condition, the rate of approximation of the operator is calculated. The study further involves the graphical representation of the convergence of the Szasz-Mirakyan-Kantorovich operator to selected continuous functions. The margins of error in the approximation of the function are tabulated. Subsequently, a novel generalized $q$-Szasz-Mirakyan-Kantorovich operator on $q$-integers is constructed, and the classical and statistical approximation properties of this new q-operator are studied.

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Cite This Article

Çiçek, H., Öztel, B., İzgi, A. (2026). A New Generalized $q$-Szasz-Mirakyan-Kantorovich Operators. Turkish Journal of Mathematics and Computer Science, Volume: 18 Issue: 3. https://doi.org/10.47000/tjmcs.1838676

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