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

Serkan Demiriz; Sezer Erdem

doi:10.33434/cams.1414791

EN

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

Abstract

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.

Keywords

Compact operators, Duals, Matrix transformations, Mersenne numbers, Sequence spaces

References

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Details

Primary Language

English

Subjects

Pure Mathematics (Other)

Journal Section

Research Article

Authors

Serkan Demiriz ^*
0000-0002-4662-6020
Türkiye

Sezer Erdem
0000-0001-9420-8264
Türkiye

Early Pub Date

February 27, 2024

Publication Date

March 4, 2024

Submission Date

January 4, 2024

Acceptance Date

February 13, 2024

Published in Issue

Year 2024 Volume: 7 Number: 1

DOI

https://doi.org/10.33434/cams.1414791

IZ

https://izlik.org/JA85WR39GN

APA

Demiriz, S., & Erdem, S. (2024). Mersenne Matrix Operator and Its Application in $p-$Summable Sequence Space. Communications in Advanced Mathematical Sciences, 7(1), 42-55. https://doi.org/10.33434/cams.1414791

AMA

1.Demiriz S, Erdem S. Mersenne Matrix Operator and Its Application in $p-$Summable Sequence Space. Communications in Advanced Mathematical Sciences. 2024;7(1):42-55. doi:10.33434/cams.1414791

Chicago

Demiriz, Serkan, and Sezer Erdem. 2024. “Mersenne Matrix Operator and Its Application in $p-$Summable Sequence Space”. Communications in Advanced Mathematical Sciences 7 (1): 42-55. https://doi.org/10.33434/cams.1414791.

EndNote

Demiriz S, Erdem S (March 1, 2024) Mersenne Matrix Operator and Its Application in $p-$Summable Sequence Space. Communications in Advanced Mathematical Sciences 7 1 42–55.

IEEE

[1]S. Demiriz and S. Erdem, “Mersenne Matrix Operator and Its Application in $p-$Summable Sequence Space”, Communications in Advanced Mathematical Sciences, vol. 7, no. 1, pp. 42–55, Mar. 2024, doi: 10.33434/cams.1414791.

ISNAD

Demiriz, Serkan - Erdem, Sezer. “Mersenne Matrix Operator and Its Application in $p-$Summable Sequence Space”. Communications in Advanced Mathematical Sciences 7/1 (March 1, 2024): 42-55. https://doi.org/10.33434/cams.1414791.

JAMA

1.Demiriz S, Erdem S. Mersenne Matrix Operator and Its Application in $p-$Summable Sequence Space. Communications in Advanced Mathematical Sciences. 2024;7:42–55.

MLA

Demiriz, Serkan, and Sezer Erdem. “Mersenne Matrix Operator and Its Application in $p-$Summable Sequence Space”. Communications in Advanced Mathematical Sciences, vol. 7, no. 1, Mar. 2024, pp. 42-55, doi:10.33434/cams.1414791.

Vancouver

1.Serkan Demiriz, Sezer Erdem. Mersenne Matrix Operator and Its Application in $p-$Summable Sequence Space. Communications in Advanced Mathematical Sciences. 2024 Mar. 1;7(1):42-55. doi:10.33434/cams.1414791

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

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

Abstract

Keywords

Abstract

References

Details

Primary Language

Subjects

Journal Section

Authors

Early Pub Date

Publication Date

Submission Date

Acceptance Date

Published in Issue

DOI

IZ

Cite

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