A Study on Lacunary $\mathcal{I-}$Statistical Convergence in Gradual Normed Linear Spaces

Hafize Gumus; Seyma Bolat

doi:10.36753/mathenot.1720763

A Study on Lacunary $\mathcal{I-}$Statistical Convergence in Gradual Normed Linear Spaces

Abstract

Following the studies on gradual numbers, which are expressed with membership functions and have many important application areas in daily life, studies on gradual normed linear spaces (GNLS) have also gained speed in recent years. On the other hand, it is thought that the definition of $\mathcal{I-}$statistical convergence, which generalizes many types of convergence, for a sequence in these spaces, and the results obtained will be important. For this reason, lacunary $\mathcal{I-}$statistical convergence in gradual normed linear spaces is defined in this paper. Therefore, more general results were obtained compared to previous studies in this area.

Keywords

$\mathcal{I-}$Convergence, $\mathcal{I-}$ statistical convergence, Gradual normed linear space, Gradual numbers, Lacunary sequences, Statistical convergence

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Details

Primary Language

English

Subjects

Mathematical Methods and Special Functions

Journal Section

Research Article

Authors

Hafize Gumus ^*
0000-0001-8972-5961
Türkiye

Seyma Bolat
0000-0002-5693-0712
Türkiye

Early Pub Date

October 25, 2025

Publication Date

December 15, 2025

Submission Date

July 6, 2025

Acceptance Date

August 25, 2025

Published in Issue

Year 2025 Volume: 13 Number: 4

DOI

https://doi.org/10.36753/mathenot.1720763

IZ

https://izlik.org/JA27BU89EK

APA

Gumus, H., & Bolat, S. (2025). A Study on Lacunary $\mathcal{I-}$Statistical Convergence in Gradual Normed Linear Spaces. Mathematical Sciences and Applications E-Notes, 13(4), 179-189. https://doi.org/10.36753/mathenot.1720763

AMA

1.Gumus H, Bolat S. A Study on Lacunary $\mathcal{I-}$Statistical Convergence in Gradual Normed Linear Spaces. Math. Sci. Appl. E-Notes. 2025;13(4):179-189. doi:10.36753/mathenot.1720763

Chicago

Gumus, Hafize, and Seyma Bolat. 2025. “A Study on Lacunary $\mathcal{I-}$Statistical Convergence in Gradual Normed Linear Spaces”. Mathematical Sciences and Applications E-Notes 13 (4): 179-89. https://doi.org/10.36753/mathenot.1720763.

EndNote

Gumus H, Bolat S (December 1, 2025) A Study on Lacunary $\mathcal{I-}$Statistical Convergence in Gradual Normed Linear Spaces. Mathematical Sciences and Applications E-Notes 13 4 179–189.

IEEE

[1]H. Gumus and S. Bolat, “A Study on Lacunary $\mathcal{I-}$Statistical Convergence in Gradual Normed Linear Spaces”, Math. Sci. Appl. E-Notes, vol. 13, no. 4, pp. 179–189, Dec. 2025, doi: 10.36753/mathenot.1720763.

ISNAD

Gumus, Hafize - Bolat, Seyma. “A Study on Lacunary $\mathcal{I-}$Statistical Convergence in Gradual Normed Linear Spaces”. Mathematical Sciences and Applications E-Notes 13/4 (December 1, 2025): 179-189. https://doi.org/10.36753/mathenot.1720763.

JAMA

1.Gumus H, Bolat S. A Study on Lacunary $\mathcal{I-}$Statistical Convergence in Gradual Normed Linear Spaces. Math. Sci. Appl. E-Notes. 2025;13:179–189.

MLA

Gumus, Hafize, and Seyma Bolat. “A Study on Lacunary $\mathcal{I-}$Statistical Convergence in Gradual Normed Linear Spaces”. Mathematical Sciences and Applications E-Notes, vol. 13, no. 4, Dec. 2025, pp. 179-8, doi:10.36753/mathenot.1720763.

Vancouver

1.Hafize Gumus, Seyma Bolat. A Study on Lacunary $\mathcal{I-}$Statistical Convergence in Gradual Normed Linear Spaces. Math. Sci. Appl. E-Notes. 2025 Dec. 1;13(4):179-8. doi:10.36753/mathenot.1720763