Geodesic
Statistical bounded sequences of bi-complex numbers
Problemy analiza, Tome 12 (2023) no. 2, pp. 3-16.

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In this paper, we extend statistical bounded sequences of real or complex numbers to the setting of sequences of bi-complex numbers. We define the statistical bounded sequence space of bi-complex numbers $b_{\infty}^{*}$ and also define the statistical bounded sequence spaces of ideals $\mathbb{I}_{\infty}^{1}$ and $\mathbb{I}_{\infty}^{2}$. We prove some inclusion relations and provide examples. We establish that $b_{\infty}^{*}$ is the direct sum of $\mathbb{I}_{\infty}^{1}$ and $ \mathbb{I}_{\infty}^{2}$. Also, we prove the decomposition theorem for statistical bounded sequences of bi-complex numbers. Finally, summability properties in the light of J.A. Fridy's work are studied.
Keywords: natural density, bi-complex, statistical bounded
Mots-clés : norm. 
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S. Bera; B. Ch. Tripathy. Statistical bounded sequences of bi-complex numbers. Problemy analiza, Tome 12 (2023) no. 2, pp. 3-16. http://geodesic.mathdoc.fr/item/PA_2023_12_2_a0/

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