A New Generalization of Sz´asz Operators

Harun Çiçek; Naıruz Ousman; Aydın İzgi

doi:10.53570/jnt.1753639

A New Generalization of Sz´asz Operators

Abstract

The purpose of this study is to define a new generalization of Sz\'{a}sz operators. The paper proceeds to study the rate of convergence and approximation properties of the newly defined Sz\'{a}sz operator on closed subintervals of the real axis. Subsequently, it investigates the Voronovskaja-type approximation and the local approximation of the new Sz\'{a}sz operator using functions satisfying the Lipschitz condition. Additionally, this paper analyzes the rate of convergence for $\digamma$ and $\digamma^\prime$ using the continuity modulus. Finally, it graphically illustrates the approximation of the new generalization of the Sz\'{a}sz operator to a continuous function with a numerical example and provides a numerical table of error values in the approximation of a continuous function for different values of $n$ and $q$.

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

Naıruz Ousman
0000-0002-7542-3556
Türkiye

Aydın İzgi
0000-0003-3715-8621
Türkiye

Early Pub Date

September 30, 2025

Publication Date

September 30, 2025

Submission Date

July 29, 2025

Acceptance Date

September 7, 2025

Published in Issue

Year 2025 Number: 52

DOI

https://doi.org/10.53570/jnt.1753639

IZ

https://izlik.org/JA84LT23DG

Cite

RIS / Bibtex

APA

Çiçek, H., Ousman, N., & İzgi, A. (2025). A New Generalization of Sz´asz Operators. Journal of New Theory, 52, 61-71. https://doi.org/10.53570/jnt.1753639

AMA

1.Çiçek H, Ousman N, İzgi A. A New Generalization of Sz´asz Operators. JNT. 2025;(52):61-71. doi:10.53570/jnt.1753639

Chicago

Çiçek, Harun, Naıruz Ousman, and Aydın İzgi. 2025. “A New Generalization of Sz´asz Operators”. Journal of New Theory, nos. 52: 61-71. https://doi.org/10.53570/jnt.1753639.

EndNote

Çiçek H, Ousman N, İzgi A (September 1, 2025) A New Generalization of Sz´asz Operators. Journal of New Theory 52 61–71.

IEEE

[1]H. Çiçek, N. Ousman, and A. İzgi, “A New Generalization of Sz´asz Operators”, JNT, no. 52, pp. 61–71, Sept. 2025, doi: 10.53570/jnt.1753639.

ISNAD

Çiçek, Harun - Ousman, Naıruz - İzgi, Aydın. “A New Generalization of Sz´asz Operators”. Journal of New Theory. 52 (September 1, 2025): 61-71. https://doi.org/10.53570/jnt.1753639.

JAMA

1.Çiçek H, Ousman N, İzgi A. A New Generalization of Sz´asz Operators. JNT. 2025;:61–71.

MLA

Çiçek, Harun, et al. “A New Generalization of Sz´asz Operators”. Journal of New Theory, no. 52, Sept. 2025, pp. 61-71, doi:10.53570/jnt.1753639.

Vancouver

1.Harun Çiçek, Naıruz Ousman, Aydın İzgi. A New Generalization of Sz´asz Operators. JNT. 2025 Sep. 1;(52):61-7. doi:10.53570/jnt.1753639