Rough statistical convergence for double sequences in L-fuzzy normed spaces

Aykut OR; Ahmet Çakı; Aykut OR; Ahmet Çakı

doi:10.3934/math.2026172

AIMS Mathematics

2026, Volume 11, Issue 2: 4283-4298. doi: 10.3934/math.2026172

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Research article

Rough statistical convergence for double sequences in L-fuzzy normed spaces

Aykut OR ^,,
Ahmet Çakı

Department of Mathematics, Faculty of Science, Çanakkale Onsekiz Mart University, 17100, Çanakkale, Türkiye

Received: 03 October 2025 Revised: 17 January 2026 Accepted: 28 January 2026 Published: 12 February 2026
MSC : 03E72, 06D72, 40A05

In this paper, we introduce and study the concept of rough statistical convergence for double sequences in L-fuzzy normed spaces. We define the rough statistical limit points of a double sequence and prove that the set is closed and convex. In addition, we define rough statistical cluster points of a double sequence, and we prove that this set is closed. Afterward, we investigate the relationships among rough statistical convergence for double sequences, related notions such as rough statistical boundedness, and rough statistical Cauchy-type conditions.
- L-fuzzy normed space,
- statistical convergence,
- rough convergence,
- rough statistical limit set
Citation: Aykut OR, Ahmet Çakı. Rough statistical convergence for double sequences in L-fuzzy normed spaces[J]. AIMS Mathematics, 2026, 11(2): 4283-4298. doi: 10.3934/math.2026172

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Abstract

In this paper, we introduce and study the concept of rough statistical convergence for double sequences in L-fuzzy normed spaces. We define the rough statistical limit points of a double sequence and prove that the set is closed and convex. In addition, we define rough statistical cluster points of a double sequence, and we prove that this set is closed. Afterward, we investigate the relationships among rough statistical convergence for double sequences, related notions such as rough statistical boundedness, and rough statistical Cauchy-type conditions.

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