Approximation Theorems and $\mathcal{I}$-Equi Statistical Convergence

Fadime Dirik; Kamil Demirci; Sevda Yıldız

doi:10.31801/cfsuasmas.1699182

Approximation Theorems and $\mathcal{I}$-Equi Statistical Convergence

Abstract

In the present work, a novel type of convergence is introduced by incorporating the notions of $\mathcal{I}$-statistical convergence and equi-statistical convergence. These offer a more extensive framework in comparison to the classical concepts of $\mathcal{I}$-convergence and statistical convergence. Within this generalized setting, two fundamental approximation results are established and proven: one in the sense of Korovkin-type theorems and another in the sense of a Voronovskaya-type result. Moreover, the paper provides a concrete example that illustrates the practical significance of the new convergence concept. Finally, an estimate for the rate at which $\mathcal{I}$-equi-statistical convergence occurs is provided, thus quantifying the efficiency of approximation under this framework.

Keywords

References

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Details

Primary Language

English

Subjects

Approximation Theory and Asymptotic Methods

Journal Section

Research Article

Authors

Fadime Dirik ^*
0000-0002-9316-9037
Türkiye

Kamil Demirci
0000-0002-5976-9768
Türkiye

Sevda Yıldız
0000-0002-4730-2271
Türkiye

Publication Date

June 30, 2026

Submission Date

May 14, 2025

Acceptance Date

September 9, 2025

Published in Issue

Year 2026 Volume: 75 Number: 2

DOI

https://doi.org/10.31801/cfsuasmas.1699182

IZ

https://izlik.org/JA66PZ38EH

Cite

RIS / Bibtex

APA

Dirik, F., Demirci, K., & Yıldız, S. (2026). Approximation Theorems and $\mathcal{I}$-Equi Statistical Convergence. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 75(2), 196-210. https://doi.org/10.31801/cfsuasmas.1699182

AMA

1.Dirik F, Demirci K, Yıldız S. Approximation Theorems and $\mathcal{I}$-Equi Statistical Convergence. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2026;75(2):196-210. doi:10.31801/cfsuasmas.1699182

Chicago

Dirik, Fadime, Kamil Demirci, and Sevda Yıldız. 2026. “Approximation Theorems and $\mathcal{I}$-Equi Statistical Convergence”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 75 (2): 196-210. https://doi.org/10.31801/cfsuasmas.1699182.

EndNote

Dirik F, Demirci K, Yıldız S (June 1, 2026) Approximation Theorems and $\mathcal{I}$-Equi Statistical Convergence. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 75 2 196–210.

IEEE

[1]F. Dirik, K. Demirci, and S. Yıldız, “Approximation Theorems and $\mathcal{I}$-Equi Statistical Convergence”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 75, no. 2, pp. 196–210, June 2026, doi: 10.31801/cfsuasmas.1699182.

ISNAD

Dirik, Fadime - Demirci, Kamil - Yıldız, Sevda. “Approximation Theorems and $\mathcal{I}$-Equi Statistical Convergence”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 75/2 (June 1, 2026): 196-210. https://doi.org/10.31801/cfsuasmas.1699182.

JAMA

1.Dirik F, Demirci K, Yıldız S. Approximation Theorems and $\mathcal{I}$-Equi Statistical Convergence. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2026;75:196–210.

MLA

Dirik, Fadime, et al. “Approximation Theorems and $\mathcal{I}$-Equi Statistical Convergence”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 75, no. 2, June 2026, pp. 196-10, doi:10.31801/cfsuasmas.1699182.

Vancouver

1.Fadime Dirik, Kamil Demirci, Sevda Yıldız. Approximation Theorems and $\mathcal{I}$-Equi Statistical Convergence. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2026 Jun. 1;75(2):196-210. doi:10.31801/cfsuasmas.1699182