On some Geometric Properties of Some Catalan Sequence Spaces

Yılmaz Yılmaz; Seçkin Yalçın; Halise Levent; Hacer Bozkurt

doi:10.47000/tjmcs.1690548

On some Geometric Properties of Some Catalan Sequence Spaces

Abstract

It is important to know whether a Banach space is rotund or smooth when examining the structural properties of the space, especially its geometric properties. Gateaux differentiability of the norm of the space has an important place in the discussion of smoothness. In this study, we examined such properties of the sequence spaces $\ell _{p}(\widetilde{C}),$ $1\leq p<\infty ,$ and $\ell _{\infty }(\widetilde{C})$ constructed by the sequence of Catalan numbers. We have also shown that some types of these spaces have elite structural properties such as Approximation and Dunford-Pettis Properties.

Keywords

References

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İlkhan, M., A new conservative matrix derived by Catalan numbers and its matrix domain in the spaces c and c0, Linear Multilinear Algebra, 68(2)(2020), 417–434.
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Details

Primary Language

English

Subjects

Operator Algebras and Functional Analysis

Journal Section

Research Article

Authors

Yılmaz Yılmaz
0000-0003-1484-782X
Türkiye

Seçkin Yalçın ^*
0000-0002-1673-3319
Türkiye

Halise Levent
0000-0002-7139-361X
Türkiye

Hacer Bozkurt
0000-0002-2216-2516
Türkiye

Publication Date

December 30, 2025

Submission Date

May 3, 2025

Acceptance Date

September 3, 2025

Published in Issue

Year 2025 Volume: 17 Number: 2

DOI

https://doi.org/10.47000/tjmcs.1690548

IZ

https://izlik.org/JA48PR35TR

Cite

RIS / Bibtex

APA

Yılmaz, Y., Yalçın, S., Levent, H., & Bozkurt, H. (2025). On some Geometric Properties of Some Catalan Sequence Spaces. Turkish Journal of Mathematics and Computer Science, 17(2), 485-495. https://doi.org/10.47000/tjmcs.1690548

AMA

1.Yılmaz Y, Yalçın S, Levent H, Bozkurt H. On some Geometric Properties of Some Catalan Sequence Spaces. TJMCS. 2025;17(2):485-495. doi:10.47000/tjmcs.1690548

Chicago

Yılmaz, Yılmaz, Seçkin Yalçın, Halise Levent, and Hacer Bozkurt. 2025. “On Some Geometric Properties of Some Catalan Sequence Spaces”. Turkish Journal of Mathematics and Computer Science 17 (2): 485-95. https://doi.org/10.47000/tjmcs.1690548.

EndNote

Yılmaz Y, Yalçın S, Levent H, Bozkurt H (December 1, 2025) On some Geometric Properties of Some Catalan Sequence Spaces. Turkish Journal of Mathematics and Computer Science 17 2 485–495.

IEEE

[1]Y. Yılmaz, S. Yalçın, H. Levent, and H. Bozkurt, “On some Geometric Properties of Some Catalan Sequence Spaces”, TJMCS, vol. 17, no. 2, pp. 485–495, Dec. 2025, doi: 10.47000/tjmcs.1690548.

ISNAD

Yılmaz, Yılmaz - Yalçın, Seçkin - Levent, Halise - Bozkurt, Hacer. “On Some Geometric Properties of Some Catalan Sequence Spaces”. Turkish Journal of Mathematics and Computer Science 17/2 (December 1, 2025): 485-495. https://doi.org/10.47000/tjmcs.1690548.

JAMA

1.Yılmaz Y, Yalçın S, Levent H, Bozkurt H. On some Geometric Properties of Some Catalan Sequence Spaces. TJMCS. 2025;17:485–495.

MLA

Yılmaz, Yılmaz, et al. “On Some Geometric Properties of Some Catalan Sequence Spaces”. Turkish Journal of Mathematics and Computer Science, vol. 17, no. 2, Dec. 2025, pp. 485-9, doi:10.47000/tjmcs.1690548.

Vancouver

1.Yılmaz Yılmaz, Seçkin Yalçın, Halise Levent, Hacer Bozkurt. On some Geometric Properties of Some Catalan Sequence Spaces. TJMCS. 2025 Dec. 1;17(2):485-9. doi:10.47000/tjmcs.1690548