On the Domain of 4-Dimensional Catalan Matrix in the Space of Absolutely Summable Double Sequences

Sezer Erdem; Serkan Demiriz

doi:10.32323/ujma.1734157

On the Domain of 4-Dimensional Catalan Matrix in the Space of Absolutely Summable Double Sequences

Abstract

The primary objective of this study is to construct a novel double sequence space by utilizing the domain of a 4-dimensional (4D) matrix in the space $\mathcal{L}_u$ of the absolutely summable double sequences defined via the well-known Catalan numbers. Within this framework, various algebraic and topological properties of the newly introduced space are investigated. The study further aims to compute the $\alpha$-, $\beta(bp)$-, and $\gamma$-duals of the space. Another essential part of the research involves characterizing certain classes of matrix transformations from the newly defined space to some classical double sequence spaces and vice versa. These contributions are expected to enrich the theory of sequence spaces and matrix transformations by introducing new insights based on special integer sequences.

Keywords

Catalan numbers, Double sequence space, Matrix transformations

References

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Details

Primary Language

English

Subjects

Pure Mathematics (Other)

Journal Section

Research Article

Authors

Sezer Erdem ^*
0000-0001-9420-8264
Türkiye

Serkan Demiriz
0000-0002-4662-6020
Türkiye

Early Pub Date

September 5, 2025

Publication Date

September 17, 2025

Submission Date

July 3, 2025

Acceptance Date

September 3, 2025

Published in Issue

Year 2025 Volume: 8 Number: 3

DOI

https://doi.org/10.32323/ujma.1734157

IZ

https://izlik.org/JA48MF98BX

APA

Erdem, S., & Demiriz, S. (2025). On the Domain of 4-Dimensional Catalan Matrix in the Space of Absolutely Summable Double Sequences. Universal Journal of Mathematics and Applications, 8(3), 141-148. https://doi.org/10.32323/ujma.1734157

AMA

1.Erdem S, Demiriz S. On the Domain of 4-Dimensional Catalan Matrix in the Space of Absolutely Summable Double Sequences. Univ. J. Math. Appl. 2025;8(3):141-148. doi:10.32323/ujma.1734157

Chicago

Erdem, Sezer, and Serkan Demiriz. 2025. “On the Domain of 4-Dimensional Catalan Matrix in the Space of Absolutely Summable Double Sequences”. Universal Journal of Mathematics and Applications 8 (3): 141-48. https://doi.org/10.32323/ujma.1734157.

EndNote

Erdem S, Demiriz S (September 1, 2025) On the Domain of 4-Dimensional Catalan Matrix in the Space of Absolutely Summable Double Sequences. Universal Journal of Mathematics and Applications 8 3 141–148.

IEEE

[1]S. Erdem and S. Demiriz, “On the Domain of 4-Dimensional Catalan Matrix in the Space of Absolutely Summable Double Sequences”, Univ. J. Math. Appl., vol. 8, no. 3, pp. 141–148, Sept. 2025, doi: 10.32323/ujma.1734157.

ISNAD

Erdem, Sezer - Demiriz, Serkan. “On the Domain of 4-Dimensional Catalan Matrix in the Space of Absolutely Summable Double Sequences”. Universal Journal of Mathematics and Applications 8/3 (September 1, 2025): 141-148. https://doi.org/10.32323/ujma.1734157.

JAMA

1.Erdem S, Demiriz S. On the Domain of 4-Dimensional Catalan Matrix in the Space of Absolutely Summable Double Sequences. Univ. J. Math. Appl. 2025;8:141–148.

MLA

Erdem, Sezer, and Serkan Demiriz. “On the Domain of 4-Dimensional Catalan Matrix in the Space of Absolutely Summable Double Sequences”. Universal Journal of Mathematics and Applications, vol. 8, no. 3, Sept. 2025, pp. 141-8, doi:10.32323/ujma.1734157.

Vancouver

1.Sezer Erdem, Serkan Demiriz. On the Domain of 4-Dimensional Catalan Matrix in the Space of Absolutely Summable Double Sequences. Univ. J. Math. Appl. 2025 Sep. 1;8(3):141-8. doi:10.32323/ujma.1734157