A New Paranormed Sequence Space Defined by Regular Bell Matrix

Karakaş, Murat; Dağlı, Muhammet Cihat

doi:10.56405/dngcrj.2023.08.01.03

dngcrj

2023

DOI: 10.56405/dngcrj.2023.08.01.03

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A New Paranormed Sequence Space Defined by Regular Bell Matrix

Murat Karakaş,

Muhammet Cihat Dağlı

Abstract: This paper aims to construct a new paranormed sequence space by the aid of a regular matrix of Bell numbers. As well, its special duals such as α−,β−,γ− duals are presented and Schauder basis is determined. Moreover, certain matrix classes for this space are characterized.

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2024

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Mersenne Matrix Operator and Its Application in $p-$Summable Sequence Space

DEMİRİZ,

ERDEM

2024

Communications in Advanced Mathematical Sciences

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In this study, it is introduced the regular Mersenne matrix operator which is obtained by using Mersenne numbers and examined sequence spaces described as the domain of this matrix in the space of $p$-summable sequences for $1\leq p \leq \infty$. After that, it investigated some properties and inclusion relations, established the Schauder basis, and stated $\alpha-$, $\beta-$, and $\gamma-$duals of the aforementioned spaces. Additionally, it is characterized by the matrix classes from newly described spaces to classical sequence spaces. Finally, we studied the compactness of matrix operators on related sequence spaces.

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Mersenne Matrix Operator and Its Application in $p-$Summable Sequence Space

DEMİRİZ,

ERDEM

2024

Communications in Advanced Mathematical Sciences

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A New Paranormed Sequence Space Defined by Regular Bell Matrix

Abstract: This paper aims to construct a new paranormed sequence space by the aid of a regular matrix of Bell numbers. As well, its special duals such as α−,β−,γ− duals are presented and Schauder basis is determined. Moreover, certain matrix classes for this space are characterized.

Cited by 1 publication

References 28 publications

Mersenne Matrix Operator and Its Application in $p-$Summable Sequence Space

Mersenne Matrix Operator and Its Application in $p-$Summable Sequence Space

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