Korovkin Type Theorem for Modified Bernstein Operators via A-Statistical Convergence and Power Summability Method

Tuğba Değirmenci; Merve Ilkhan Kara

doi:10.36753/mathenot.1657527

EN

Korovkin Type Theorem for Modified Bernstein Operators via A-Statistical Convergence and Power Summability Method

Abstract

In this study, we investigate the approximation properties of modified Bernstein operators through the lens of A-statistical convergence and power summability methods. Our main objective is to establish a Korovkin-type approximation theorem in this generalized setting. By incorporating statistical convergence, we aim to provide broader and more powerful approximation results that can be applied in various contexts where classical convergence criteria may fail or be insufficient.

Keywords

A-statistical convergence, Bernstein operators, Korovkin type theorem, Power summability method

References

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Details

Primary Language

English

Subjects

Approximation Theory and Asymptotic Methods

Journal Section

Research Article

Authors

Tuğba Değirmenci
0000-0003-2826-9741
Türkiye

Merve Ilkhan Kara ^*
0000-0002-0831-1474
Türkiye

Early Pub Date

June 11, 2025

Publication Date

June 26, 2025

Submission Date

March 13, 2025

Acceptance Date

June 10, 2025

Published in Issue

Year 2025 Volume: 13 Number: 2

DOI

https://doi.org/10.36753/mathenot.1657527

IZ

https://izlik.org/JA62ZY46CU

APA

Değirmenci, T., & Ilkhan Kara, M. (2025). Korovkin Type Theorem for Modified Bernstein Operators via A-Statistical Convergence and Power Summability Method. Mathematical Sciences and Applications E-Notes, 13(2), 84-91. https://doi.org/10.36753/mathenot.1657527

AMA

1.Değirmenci T, Ilkhan Kara M. Korovkin Type Theorem for Modified Bernstein Operators via A-Statistical Convergence and Power Summability Method. Math. Sci. Appl. E-Notes. 2025;13(2):84-91. doi:10.36753/mathenot.1657527

Chicago

Değirmenci, Tuğba, and Merve Ilkhan Kara. 2025. “Korovkin Type Theorem for Modified Bernstein Operators via A-Statistical Convergence and Power Summability Method”. Mathematical Sciences and Applications E-Notes 13 (2): 84-91. https://doi.org/10.36753/mathenot.1657527.

EndNote

Değirmenci T, Ilkhan Kara M (June 1, 2025) Korovkin Type Theorem for Modified Bernstein Operators via A-Statistical Convergence and Power Summability Method. Mathematical Sciences and Applications E-Notes 13 2 84–91.

IEEE

[1]T. Değirmenci and M. Ilkhan Kara, “Korovkin Type Theorem for Modified Bernstein Operators via A-Statistical Convergence and Power Summability Method”, Math. Sci. Appl. E-Notes, vol. 13, no. 2, pp. 84–91, June 2025, doi: 10.36753/mathenot.1657527.

ISNAD

Değirmenci, Tuğba - Ilkhan Kara, Merve. “Korovkin Type Theorem for Modified Bernstein Operators via A-Statistical Convergence and Power Summability Method”. Mathematical Sciences and Applications E-Notes 13/2 (June 1, 2025): 84-91. https://doi.org/10.36753/mathenot.1657527.

JAMA

1.Değirmenci T, Ilkhan Kara M. Korovkin Type Theorem for Modified Bernstein Operators via A-Statistical Convergence and Power Summability Method. Math. Sci. Appl. E-Notes. 2025;13:84–91.

MLA

Değirmenci, Tuğba, and Merve Ilkhan Kara. “Korovkin Type Theorem for Modified Bernstein Operators via A-Statistical Convergence and Power Summability Method”. Mathematical Sciences and Applications E-Notes, vol. 13, no. 2, June 2025, pp. 84-91, doi:10.36753/mathenot.1657527.

Vancouver

1.Tuğba Değirmenci, Merve Ilkhan Kara. Korovkin Type Theorem for Modified Bernstein Operators via A-Statistical Convergence and Power Summability Method. Math. Sci. Appl. E-Notes. 2025 Jun. 1;13(2):84-91. doi:10.36753/mathenot.1657527