New Perspectives on Generalised Lacunary Statistical Convergence of Multiset Sequences

New Perspectives on Generalised Lacunary Statistical Convergence of Multiset Sequences

This paper explores the concepts of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="fraktur">J</mi></semantics></math></inline-formula>-lacunary statistical lim...

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Bibliographic Details
Main Authors:	María C. Listán-García, Ömer Kişi, Mehmet Gürdal
Format:	Article
Language:	English
Published:	MDPI AG 2025-01-01
Series:	Mathematics
Subjects:	multiset sequences \({\mathfrak{J}}\)-lacunary statistical Cauchy \({\mathcal{I}^{\ast}}\)-lacunary statistical Cauchy \({\mathfrak{J}}\)-lacunary statistical limit point \({\mathfrak{J}}\)-lacunary statistical cluster point
Online Access:	https://www.mdpi.com/2227-7390/13/1/164
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Summary:	This paper explores the concepts of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="fraktur">J</mi></semantics></math></inline-formula>-lacunary statistical limit points, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="fraktur">J</mi></semantics></math></inline-formula>-lacunary statistical cluster points, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="fraktur">J</mi></semantics></math></inline-formula>-lacunary statistical Cauchy multiset sequences. Building upon previous work in the field, we investigate the relationships between <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="fraktur">J</mi></semantics></math></inline-formula>-lacunary statistical convergence and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi mathvariant="fraktur">J</mi><mo>*</mo></msup></semantics></math></inline-formula>-lacunary statistical convergence in multiset sequences. The findings contribute to a deeper understanding of the convergence behaviour of multiset sequences and provide new insights into the application of ideal convergence in this context.
ISSN:	2227-7390