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

Year 2025, Volume: 13 Issue: 3, 144 - 155, 06.09.2025

Funda Babaarslan

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

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

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