• Journal of applied mathematics & informatics
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• v.41 no.3
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• pp.541-552
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• 2023

In 2005, Patterson studied lacunary statistical convergence of double sequences of real numbers and, in 2009, Mursaleen introduced notion of lacunary statistical convergence of single sequences in intuitionistic fuzzy normed space. The current work intends to investigate the lacunary statistical convergence of double sequences and some significant conclusions on the algebra of the lacunary statistical limit of double sequences in intuitionistic fuzzy normed space. In addition, we have studied some examples to support the definitions.

• Honam Mathematical Journal
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• v.45 no.3
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• pp.503-512
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• 2023

In the present article, we introduce the concepts of strongly asymptotically lacunary equivalence, asymptotically statistical equivalence, and asymptotically lacunary statistical equivalence for sequences in g-metric spaces. We investigate some properties and relationships among these new concepts.

• Honam Mathematical Journal
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• v.46 no.2
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• pp.291-306
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• 2024

The concept of lacunary statistical convergence of triple sequences with respect to gradual 2-normed linear spaces is introduced in this research. We learn about its link to some inclusion and fundamental properties. The notion of lacunary statistical Cauchy triple sequences is introduced in the conclusion, and it is demonstrated that it is equivalent to the idea of lacunary statistical convergence.

• Kyungpook Mathematical Journal
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• v.50 no.4
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• pp.565-574
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• 2010

In this paper we introduce the concept of lacunary statistical and lacunary strongly convergence of generalized difference sequence of fuzzy real numbers. We prove some inclusion relations and also study some of their properties.

• Journal of applied mathematics & informatics
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• v.39 no.3_4
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• pp.303-319
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• 2021

In this paper, we introduce the concepts of Wijsman strongly p-lacunary summability of order 𝛼, Wijsman lacunary statistical convergence of order 𝛼 and Hausdorff lacunary statistical convergence of order 𝛼 for double set sequences. Also, we investigate some properties of these new concepts and examine the existence of some relationships between them. Furthermore, we study the relationships between these new concepts and some concepts in the literature.

• Korean Journal of Mathematics
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• v.31 no.3
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• pp.349-361
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• 2023

In this article, we construct lacunary ∆^m-statistical convergence for triple sequences within the context of intuitionistic fuzzy n-normed spaces (IFnNS). For lacunary ∆^m-statistical convergence of triple sequence in IFnNS, we demonstrate numerous results. For this innovative notion of convergence, we further built lacunary ∆^m-statistical Cauchy sequences and offered the Cauchy convergence criterion.

• Journal of applied mathematics & informatics
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• v.40 no.1_2
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• pp.215-231
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• 2022

In this paper, for double set sequences, as a new approach to the notion of Wijsman asymptotical lacunary statistical equivalence of order 𝜂, we introduce new concepts which are called Wijsman asymptotical ${\mathcal{I}}_2$-lacunary statistical equivalence of order 𝜂 and Wijsman asymptotical strong ${\mathcal{I}}_2$-lacunary equivalence of order 𝜂 where 0 < 𝜂 ≤ 1. Also, some properties of these new concepts are investigated, and the existence of some relations between these and some previously studied asymptotical equivalence concepts for double set sequences is examined.

• Kyungpook Mathematical Journal
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• v.52 no.4
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• pp.473-482
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• 2012

In this article we introduce the concepts of lacunary I-convergent sequences. We investigate its different properties like solid, symmetric, convergence free etc.

• Journal of applied mathematics & informatics
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• v.40 no.3_4
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• pp.433-444
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• 2022

In the present paper, we introduce some new notions of Wijsman ${\mathcal{I}}$-statistical convergence with the use of Orlicz function, lacunary sequence and triple sequences of sets, and obtain some analogous results from the new definitions point of views.

• Communications of the Korean Mathematical Society
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• v.23 no.2
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• pp.179-185
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• 2008

In this paper we introduce and study lacunary statistical convergence for double sequences of fuzzy numbers and we shall also present some inclusion theorems.