Ideal convergence in modified IFNS and $ \mathcal{L} $-fuzzy normed space

Vakeel A. Khan; Mikail Et; Izhar Ali Khan

doi:10.3934/mfc.2023044

Article Contents

2025, Volume 8, Issue 4: 492-506. Doi: 10.3934/mfc.2023044

This issue Previous Article Topological and geometric properties of some new sequence spaces of generalized difference operator Next Article Locally dually flatness properties in cubic $ (\alpha, \beta) $-Metric

Ideal convergence in modified IFNS and $ \mathcal{L} $-fuzzy normed space

1.
Department of Mathematics, Aligarh Muslim University, Aligarh–202002, India
2.
Department of Mathematics, Firat University, Elâzığ–23119, Turkey
3.
Department of Mathematics, School of Basic Sciences, CSJM University, Kanpur–208024, India

^*Corresponding author: Mikail Et
^*Corresponding author: Mikail Et

Received: March 2023

Revised: September 2023

Early access: November 2023

Published: August 2025

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Abstract

This paper aims to present the concept of $ I $ & $ I^* $ convergence and $ s_p $- $ I $ convergence along with the $ I $ Cauchy criterion in $ \mathcal{L} $-fuzzy normed space (in short $ \mathcal{L} $-FNS). Characterizations of these notions in $ \mathcal{L} $-FNS have been shown in the paper. This paper also presents how these notions are related to each other in $ \mathcal{L} $-FNS. We have also given certain important counter-examples to establish the relationships between them. In addition, we introduce the $ \mathcal{L} $ -fuzzy limit points and $ \mathcal{L} $-fuzzy cluster points of a sequence in $ \mathcal{L} $-FNS.

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Mathematics Subject Classification: Primary: 40A05, 40A35; Secondary: 54E99.

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