• Journal of applied mathematics & informatics
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• v.40 no.1_2
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• pp.191-204
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• 2022

This paper introduces the statistical convergence concepts of double sequences of complex uncertain variables: statistical convergence almost surely(a.s.), statistical convergence in measure, statistical convergence in mean, statistical convergence in distribution and statistical convergence uniformly almost surely(u.a.s.).

• Honam Mathematical Journal
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• v.43 no.3
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• pp.417-431
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• 2021

In this study, we introduced the notions of rough statistical convergence and defined the set of rough statistical limit points of a sequence and obtained statistical convergence criteria associated with this set in 2-normed space. Then, we proved that this set is closed and convex in 2-normed space. Also, we examined the relations between the set of statistical cluster points and the set of rough statistical limit points of a sequence in 2-normed space.

• 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.

• Kyungpook Mathematical Journal
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• v.56 no.2
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• pp.357-366
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• 2016

In this paper, deferred statistical convergence is defined by using deferred $Ces{\grave{a}}ro$ mean instead of $Ces{\grave{a}}ro$ mean in the definition of statistical convergence. The obtained method is compared with strong deferred $Ces{\grave{a}}ro$ mean and statistical convergence under some certain assumptions. Also, some inclusion theorems and examples are given.

• Korean Journal of Mathematics
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• v.30 no.1
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• pp.155-160
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• 2022

Let X be a partial metric space generated by a partial metric p. In this paper, we introduce the notions of statistical convergence and strongly Cesàro summability in partial metric spaces. Also, we investigate the relations between the statistical convergence and strongly Cesàro summability.

• Honam Mathematical Journal
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• v.44 no.1
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• pp.110-120
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• 2022

In this paper, we introduce the concepts of Wijsman invariant statistical, Wijsman deferred invariant statistical and Wijsman strongly deferred invariant convergence of order 𝜂 (0 < 𝜂 ≤ 1) for set sequences. Also, we investigate some properties of these concepts and some relationships between them.

• 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.

• Honam Mathematical Journal
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• v.43 no.1
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• pp.47-58
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• 2021

In this paper, we introduce rough statistical convergence of difference double sequences in normed linear spaces as an extension of rough convergence. We define the set of rough statistical limit points of a difference double sequence and analyze the results with proofs.

• 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.

• Journal of applied mathematics & informatics
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• v.29 no.3_4
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• pp.1017-1025
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• 2011

In this paper, we survey various notions and results related to statistical convergence of a sequence of fuzzy numbers, in which statistical convergence for fuzzy numbers was first introduced by Nuray and Savas in 1995. We will go over boundedness, convergence of sequences of fuzzy numbers, statistically convergence and statistically Cauchy sequences of fuzzy numbers, statistical limit and cluster point for sequences of fuzzy numbers, statistical mono-tonicity and boundedness of a sequence of fuzzy numbers and finally statistical limit inferior and limit inferior for the statistically bounded sequences of fuzzy numbers.