On lacunary A^{I}-statistical convergence of fuzzy triple sequences of order γ

Abstract

In this study, we propose the concepts of $f$-lacunary $A^{\mathcal{I}}$-statistical convergence of order $\gamma$ and strongly $f$-lacunary $A^{\mathcal{I}}$-summability of order $\gamma$ for triple sequences of fuzzy numbers. Additionally, we explore fundamental connections between these convergence notions. As a practical application, we apply this newly defined convergence to establish a fuzzy Korovkin-type approximation theorem concerning triple sequences of fuzzy positive linear operators. To highlight the effectiveness of our result, we provide an example that demonstrates the superiority of the established theorem over its classical counterpart.