Statistical bounded sequences of bi-complex numbers

S. Bera ; B. Ch. Tripathy

Problemy analiza, Tome 12 (2023) no. 2, pp. 3-16

Résumé

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.

Détail

Keywords: natural density, bi-complex, statistical bounded
Mots-clés : norm.