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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Published in | Issues of analysis Vol. 30; no. 2; pp. 3 - 16 |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
Petrozavodsk State University
01.06.2023
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Subjects | |
Online Access | Get full text |
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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. |
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ISSN: | 2306-3432 2306-3424 2306-3432 |
DOI: | 10.15393/j3.art.2023.13090 |