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 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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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 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.
AbstractList 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.
Author Bera, S.
Tripathy, B. Ch
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Snippet 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...
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SubjectTerms bi-complex
natural density
norm
statistical bounded
Title STATISTICAL BOUNDED SEQUENCES OF BI-COMPLEX NUMBERS
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