New types of convergence of double sequences in neutrosophic fuzzy \(G\)-metric spaces

Volume 17, Issue 4, pp 150--179 https://dx.doi.org/10.22436/jnsa.017.04.01

Publication Date: August 04, 2024 Submission Date: May 22, 2024 Revision Date: June 30, 2024 Accteptance Date: July 02, 2024

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Authors

V. A. Khan - Department of Mathematics‎, Aligarh Muslim University, Aligarh-202002, Uttar‎ ‎Pradesh, ‎India. O. Kisi - Department of Mathematics, Bartın University, Bartın-74100, Turkey. R. Akbiyik - Department of Mathematics, Bartın University, Bartın-74100, Turkey.

Abstract

‎In this study‎, ‎we present statistical convergence‎, ‎statistical limit points‎, ‎and statistical cluster points of double sequences in neutrosophic fuzzy‎ ‎\(G\)-metric space with order \(q\)‎, ‎extending the notion of neutrosophic fuzzy‎ ‎metric space‎. ‎We support our assertions with relevant theorems and elucidate‎ ‎them through illustrative examples‎. ‎Following the establishment of statistical‎ ‎convergence and the scrutiny of its properties within these spaces‎, ‎we explore‎ ‎the concepts of lacunary statistical convergence and strongly lacunary‎ ‎convergence of double sequences‎, ‎while also investigating the relationships‎ ‎among them‎. ‎

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Keywords

• Neutrosophic normed spaces
• \(g\)-metric space
• statistical convergence
• statistical Cauchy sequence
• statistical limit points
• statistical cluster points

MSC

•  40G15
•  40A05
•  03B52
•  03E72

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