On some geometric properties of sequence spaces of generalized arithmetic divisor sum function

Recently, some new sequence spaces ℓ p ( A α ) ( 0 < p < ∞ ) , c 0 ( A α ) , c ( A α ) , and ℓ ∞ ( A α ) have been studied by Yaying et al. (Forum Math., 2024 , https://doi.org/10.1515/forum-2023-0138 ) as matrix domains of A α = ( a n , v α ) , where a m , v α = { v α ρ ( α ) ( m ) , v ∣ m ,...

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Bibliographic Details
Published inJournal of inequalities and applications Vol. 2024; no. 1; pp. 128 - 10
Main Authors Mursaleen, Mohammad, Herawati, Elvina
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 27.09.2024
Springer Nature B.V
SpringerOpen
Subjects
Analysis
Applications of Mathematics
Approximation
Arithmetic divisor sum function
Geometric properties
Mathematical functions
Mathematics
Mathematics and Statistics
Operators (mathematics)
Prime numbers
Sequence spaces
47B07
Sequence spaces
Geometric properties
47B37
46A45
46B45
Arithmetic divisor sum function
40C05
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Summary:Recently, some new sequence spaces ℓ p ( A α ) ( 0 < p < ∞ ) , c 0 ( A α ) , c ( A α ) , and ℓ ∞ ( A α ) have been studied by Yaying et al. (Forum Math., 2024 , https://doi.org/10.1515/forum-2023-0138 ) as matrix domains of A α = ( a n , v α ) , where a m , v α = { v α ρ ( α ) ( m ) , v ∣ m , 0 , v ∤ m , and ρ ( α ) ( m ) : = sum of the α th power of the positive divisors of m ∈ N . They obtained their duals, matrix transformations and associated compact matrix operators for these matrix classes. This article deals with some geometric properties of these sequence spaces.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:1029-242X
1025-5834
1029-242X
DOI:10.1186/s13660-024-03208-z