An Extension of Maddox’s Paranormed Sequence Spaces with Narayana Numbers

Hacer Bilgin Ellidokuzoğlu; Serkan Demiriz

doi:10.54187/jnrs.1671958

An Extension of Maddox’s Paranormed Sequence Spaces with Narayana Numbers

Abstract

This study focuses on constructing an extended version of Maddox’s paranormed sequence spaces, denoted by $c_0(N, p)$, $c(N, p)$, $\ell_\infty(N, p)$, and $\ell(N, p)$. The study aims to define and investigate the characteristics of these sequence spaces, along with their paranormed extensions. In particular, it develops a theoretical framework for Narayana sequence spaces, establishing their topological, algebraic, and matrix transformation properties. The Schauder basis for these spaces is introduced, laying the foundation for further functional analysis. The research also examines the $alpha$-, $\beta$-, and $\gamma$- duals of these spaces and investigates the conditions under which matrix transformations preserve their structural properties. The findings highlight the equivalences between these spaces and classical sequence spaces such as $\ell_1$, $c$, and $\ell_\infty$.

Keywords

Narayana numbers, Maddox’s paranormed sequence spaces, Schauder basis, topological properties, paranormed sequence spaces

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Details

Primary Language

English

Subjects

Operator Algebras and Functional Analysis

Journal Section

Research Article

Authors

Hacer Bilgin Ellidokuzoğlu ^*
0000-0003-1658-201X
Türkiye

Serkan Demiriz
0000-0002-4662-6020
Türkiye

Publication Date

August 31, 2025

Submission Date

April 8, 2025

Acceptance Date

July 23, 2025

Published in Issue

Year 2025 Volume: 14 Number: 2

DOI

https://doi.org/10.54187/jnrs.1671958

IZ

https://izlik.org/JA63TH98AE

APA

Bilgin Ellidokuzoğlu, H., & Demiriz, S. (2025). An Extension of Maddox’s Paranormed Sequence Spaces with Narayana Numbers. Journal of New Results in Science, 14(2), 138-151. https://doi.org/10.54187/jnrs.1671958

AMA

1.Bilgin Ellidokuzoğlu H, Demiriz S. An Extension of Maddox’s Paranormed Sequence Spaces with Narayana Numbers. JNRS. 2025;14(2):138-151. doi:10.54187/jnrs.1671958

Chicago

Bilgin Ellidokuzoğlu, Hacer, and Serkan Demiriz. 2025. “An Extension of Maddox’s Paranormed Sequence Spaces With Narayana Numbers”. Journal of New Results in Science 14 (2): 138-51. https://doi.org/10.54187/jnrs.1671958.

EndNote

Bilgin Ellidokuzoğlu H, Demiriz S (August 1, 2025) An Extension of Maddox’s Paranormed Sequence Spaces with Narayana Numbers. Journal of New Results in Science 14 2 138–151.

IEEE

[1]H. Bilgin Ellidokuzoğlu and S. Demiriz, “An Extension of Maddox’s Paranormed Sequence Spaces with Narayana Numbers”, JNRS, vol. 14, no. 2, pp. 138–151, Aug. 2025, doi: 10.54187/jnrs.1671958.

ISNAD

Bilgin Ellidokuzoğlu, Hacer - Demiriz, Serkan. “An Extension of Maddox’s Paranormed Sequence Spaces With Narayana Numbers”. Journal of New Results in Science 14/2 (August 1, 2025): 138-151. https://doi.org/10.54187/jnrs.1671958.

JAMA

1.Bilgin Ellidokuzoğlu H, Demiriz S. An Extension of Maddox’s Paranormed Sequence Spaces with Narayana Numbers. JNRS. 2025;14:138–151.

MLA

Bilgin Ellidokuzoğlu, Hacer, and Serkan Demiriz. “An Extension of Maddox’s Paranormed Sequence Spaces With Narayana Numbers”. Journal of New Results in Science, vol. 14, no. 2, Aug. 2025, pp. 138-51, doi:10.54187/jnrs.1671958.

Vancouver

1.Hacer Bilgin Ellidokuzoğlu, Serkan Demiriz. An Extension of Maddox’s Paranormed Sequence Spaces with Narayana Numbers. JNRS. 2025 Aug. 1;14(2):138-51. doi:10.54187/jnrs.1671958