STATISTICAL BOUNDED SEQUENCES OF BI-COMPLEX NUMBERS

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 bicomplex numbers b^* ∞and also define the statistical bounded sequence spaces of ideals I^1 ∞ and I^2 ∞ . We prove...

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Bibliographic Details
Published inIssues of analysis Vol. 30; no. 2; pp. 3 - 16
Main Authors Bera, S., Tripathy, B. Ch
Format Journal Article
LanguageEnglish
Published Petrozavodsk State University 01.06.2023
Subjects
bi-complex
natural density
norm
statistical bounded
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Summary: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 bicomplex numbers b^* ∞and also define the statistical bounded sequence spaces of ideals I^1 ∞ and I^2 ∞ . We prove some inclusion relations and provide examples. We establish that b^* ∞ is the direct sum of I^1 ∞ and I^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.
ISSN:2306-3432
2306-3424
2306-3432
DOI:10.15393/j3.art.2023.13090