Work

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

Year: 2024

Type: article

Abstract: Recently, some new sequence spaces $\ell _{p}(\mathfrak{A}^{\alpha })$ $(0< p<\infty )$ , $c_{0}(\mathfrak{A}^{\alpha })$ , $c(\mathfrak{A}^{\alpha })$ , and $\ell _{\infty }(\mathfrak{A}^{\alpha })$ have been studied by Yaying et al. (Forum Math., 2024, https://doi.org/10.1515/forum-2023-0138 ) as matrix domains of $\mathfrak{A}^{\alpha }=(a_{n,v}^{\alpha })$ , where $$ a_{\mathfrak{m},v}^{\alpha }=\left \{ \textstyle\begin{array}{c@{\quad}c@{\quad}c} \dfrac{v^{\alpha }}{\rho ^{(\alpha )}(\mathfrak{m})} & , & v\mid \mathfrak{m}, \\ 0 & , & v\nmid \mathfrak{m},\end{array}\displaystyle \right . $$ and $\rho ^{(\alpha )}(\mathfrak{m}):=$ sum of the $\alpha ^{\text{th}}$ power of the positive divisors of $\mathfrak{m}\in \mathbb{N}$ . 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.

Source: Journal of Inequalities and Applications

DOI: 10.1186/s13660-024-03208-z

Authors: Mohammad Mursaleen, Elvina Herawati

Institutions: Aligarh Muslim University, China Medical University, Universitas Sumatera Utara, China Medical University Hospital

Language: English

Topic: Approximation Theory and Sequence Spaces

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,990

Funder: Universitas Sumatera Utara