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

Harun Çiçek; Betül Öztel; Aydın İzgi

doi:10.47000/tjmcs.1838676

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

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.

Keywords

References

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Details

Primary Language

English

Subjects

Approximation Theory and Asymptotic Methods

Journal Section

Research Article

Authors

Harun Çiçek ^*
0000-0003-3018-3015
Türkiye

Betül Öztel
0000-0002-5973-9323
Türkiye

Aydın İzgi
0000-0003-3715-8621
Türkiye

Publication Date

October 13, 2026

Submission Date

December 8, 2025

Acceptance Date

March 5, 2026

Published in Issue

Year 2026 Volume: 18 Number: 3

DOI

https://doi.org/10.47000/tjmcs.1838676

IZ

https://izlik.org/JA38BK84RE

Cite

RIS / Bibtex

APA

Çiçek, H., Öztel, B., & İzgi, A. (2026). A New Generalized $q$-Szasz-Mirakyan-Kantorovich Operators. Turkish Journal of Mathematics and Computer Science, 18(3), 665-682. https://doi.org/10.47000/tjmcs.1838676

AMA

1.Çiçek H, Öztel B, İzgi A. A New Generalized $q$-Szasz-Mirakyan-Kantorovich Operators. TJMCS. 2026;18(3):665-682. doi:10.47000/tjmcs.1838676

Chicago

Çiçek, Harun, Betül Öztel, and Aydın İzgi. 2026. “A New Generalized $q$-Szasz-Mirakyan-Kantorovich Operators”. Turkish Journal of Mathematics and Computer Science 18 (3): 665-82. https://doi.org/10.47000/tjmcs.1838676.

EndNote

Çiçek H, Öztel B, İzgi A (October 1, 2026) A New Generalized $q$-Szasz-Mirakyan-Kantorovich Operators. Turkish Journal of Mathematics and Computer Science 18 3 665–682.

IEEE

[1]H. Çiçek, B. Öztel, and A. İzgi, “A New Generalized $q$-Szasz-Mirakyan-Kantorovich Operators”, TJMCS, vol. 18, no. 3, pp. 665–682, Oct. 2026, doi: 10.47000/tjmcs.1838676.

ISNAD

Çiçek, Harun - Öztel, Betül - İzgi, Aydın. “A New Generalized $q$-Szasz-Mirakyan-Kantorovich Operators”. Turkish Journal of Mathematics and Computer Science 18/3 (October 1, 2026): 665-682. https://doi.org/10.47000/tjmcs.1838676.

JAMA

1.Çiçek H, Öztel B, İzgi A. A New Generalized $q$-Szasz-Mirakyan-Kantorovich Operators. TJMCS. 2026;18:665–682.

MLA

Çiçek, Harun, et al. “A New Generalized $q$-Szasz-Mirakyan-Kantorovich Operators”. Turkish Journal of Mathematics and Computer Science, vol. 18, no. 3, Oct. 2026, pp. 665-82, doi:10.47000/tjmcs.1838676.

Vancouver

1.Harun Çiçek, Betül Öztel, Aydın İzgi. A New Generalized $q$-Szasz-Mirakyan-Kantorovich Operators. TJMCS. 2026 Oct. 1;18(3):665-82. doi:10.47000/tjmcs.1838676