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 pro...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Petrozavodsk State University
2023-06-01
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| Series: | Проблемы анализа |
| Subjects: | |
| Online Access: | https://issuesofanalysis.petrsu.ru/article/genpdf.php?id=13090&lang=ru |
| 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: | 2306-3424 2306-3432 |