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This article is cited in 3 scientific papers (total in 3 papers)
Statistical bounded sequences of bi-complex numbers
S. Bera, B. Ch. Tripathy Department of Mathematics, Tripura University,
Suryamaninagar, Agartala-799022, Tripura(W), India
Abstract:
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, norm.
Received: 08.01.2023 Revised: 21.05.2023 Accepted: 12.05.2023
Citation:
S. Bera, B. Ch. Tripathy, “Statistical bounded sequences of bi-complex numbers”, Probl. Anal. Issues Anal., 12(30):2 (2023), 3–16
Linking options:
https://www.mathnet.ru/eng/pa372 https://www.mathnet.ru/eng/pa/v30/i2/p3
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Abstract page: | 83 | Full-text PDF : | 81 | References: | 17 |
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