Statistical Harmonic Summability of Fuzzy Fractional Difference Sequences and Associated Korovkin-Type Theorem

Funda Babaarslan

doi:10.36753/mathenot.1695015

Statistical Harmonic Summability of Fuzzy Fractional Difference Sequences and Associated Korovkin-Type Theorem

Abstract

In the present paper, we introduce the concepts of $\Delta^{f,b,a}$--harmonic summability, $\Delta^{f,b,a}$--statistical harmonic summability and $\Delta^{f,b,a}$--logarithmic statistical convergence of sequences of fuzzy numbers, where $\Delta^{f,b,a}$ is fractional difference operator introduced by Baliarsingh \cite{Bal2016}. Then, we investigate the relationship between the sorts of new definitions. Also, we give some results on limits of $\Delta^{f,b,a}$--logarithmic statistical convergence for these sequences. Finally, we use the new statistical summability method to prove a Korovkin-type approximation theorem.

Keywords

Fractional difference operator, Harmonic summability, Logarithmic convergence, Sequences of fuzzy numbers, Statistical harmonic summability

References

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Details

Primary Language

English

Subjects

Applied Mathematics (Other)

Journal Section

Research Article

Authors

Funda Babaarslan ^*
0000-0003-2716-7831
Türkiye

Early Pub Date

July 30, 2025

Publication Date

September 6, 2025

Submission Date

May 7, 2025

Acceptance Date

July 23, 2025

Published in Issue

Year 2025 Volume: 13 Number: 3

DOI

https://doi.org/10.36753/mathenot.1695015

IZ

https://izlik.org/JA43DU72CN

APA

Babaarslan, F. (2025). Statistical Harmonic Summability of Fuzzy Fractional Difference Sequences and Associated Korovkin-Type Theorem. Mathematical Sciences and Applications E-Notes, 13(3), 144-155. https://doi.org/10.36753/mathenot.1695015

AMA

1.Babaarslan F. Statistical Harmonic Summability of Fuzzy Fractional Difference Sequences and Associated Korovkin-Type Theorem. Math. Sci. Appl. E-Notes. 2025;13(3):144-155. doi:10.36753/mathenot.1695015

Chicago

Babaarslan, Funda. 2025. “Statistical Harmonic Summability of Fuzzy Fractional Difference Sequences and Associated Korovkin-Type Theorem”. Mathematical Sciences and Applications E-Notes 13 (3): 144-55. https://doi.org/10.36753/mathenot.1695015.

EndNote

Babaarslan F (September 1, 2025) Statistical Harmonic Summability of Fuzzy Fractional Difference Sequences and Associated Korovkin-Type Theorem. Mathematical Sciences and Applications E-Notes 13 3 144–155.

IEEE

[1]F. Babaarslan, “Statistical Harmonic Summability of Fuzzy Fractional Difference Sequences and Associated Korovkin-Type Theorem”, Math. Sci. Appl. E-Notes, vol. 13, no. 3, pp. 144–155, Sept. 2025, doi: 10.36753/mathenot.1695015.

ISNAD

Babaarslan, Funda. “Statistical Harmonic Summability of Fuzzy Fractional Difference Sequences and Associated Korovkin-Type Theorem”. Mathematical Sciences and Applications E-Notes 13/3 (September 1, 2025): 144-155. https://doi.org/10.36753/mathenot.1695015.

JAMA

1.Babaarslan F. Statistical Harmonic Summability of Fuzzy Fractional Difference Sequences and Associated Korovkin-Type Theorem. Math. Sci. Appl. E-Notes. 2025;13:144–155.

MLA

Babaarslan, Funda. “Statistical Harmonic Summability of Fuzzy Fractional Difference Sequences and Associated Korovkin-Type Theorem”. Mathematical Sciences and Applications E-Notes, vol. 13, no. 3, Sept. 2025, pp. 144-55, doi:10.36753/mathenot.1695015.

Vancouver

1.Funda Babaarslan. Statistical Harmonic Summability of Fuzzy Fractional Difference Sequences and Associated Korovkin-Type Theorem. Math. Sci. Appl. E-Notes. 2025 Sep. 1;13(3):144-55. doi:10.36753/mathenot.1695015