• Journal of applied mathematics & informatics
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• 제41권3호
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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.

• Kyungpook Mathematical Journal
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• 제51권4호
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• pp.385-393
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• 2011

The aim of this paper is to introduce and study the sequence spaces [w, ${\theta}$, F, p, q]$_{\infty}({\Delta}_{\upsilon}^m)$, [w, ${\theta}$, F, p, q]$_1({\Delta}_{\upsilon}^m)$ and [w, ${\theta}$, F, p, q]$_0({\Delta}_{\upsilon}^m)$, which arise from the notions of generalized difference sequence space, lacunary convergence, invariant mean and a sequence of Moduli $F=(f_k)$. We establish some inclusion relations between these spaces under some conditions.

• Journal of Applied and Pure Mathematics
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• 제5권3_4호
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• pp.265-279
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• 2023

In this paper, we firstly presented the definitions of arithmetic ${\mathcal{I}}$-statistically convergence, ${\mathcal{I}}$-lacunary arithmetic statistically convergence, strongly ${\mathcal{I}}$-lacunary arithmetic convergence, ${\mathcal{I}}$-Cesàro arithmetic summable and strongly ${\mathcal{I}}$-Cesàro arithmetic summable using weighted density via Orlicz function ${\tilde{\phi}}$. Then, we proved some theorems associated with these concepts, and we examined the relationship between them. Finally, we establish some sequential properties of ${\mathcal{I}}$-lacunary arithmetic statistical continuity.

• 호남수학학술지
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• 제43권1호
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• pp.100-114
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• 2021

In this study, we present some asymptotical invariant and asymptotical lacunary invariant equivalence types for double sequences via ideals using modulus functions and investigate relationships between them.

• 호남수학학술지
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• 제43권2호
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• pp.343-357
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• 2021

In the present paper, we introduce the concepts of $\mathcal{I}$-asymptotically statistical $\tilde{\phi}$-equivalence and $\mathcal{I}$-asymptotically lacunary statistical $\tilde{\phi}$-equivalence for triple sequences. Moreover, we give the relations between these new notions.

• Kyungpook Mathematical Journal
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• 제52권4호
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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.

• Korean Journal of Mathematics
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• 제30권4호
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• pp.679-686
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• 2022

In this study, the concept of lacunary statistical convergence is studied in G-metric spaces. The G-metric function is based on the concept of distance between three points. Considering this new concept of distance, we examined the relationships between GS, GS_θ, Gσ₁ and GN_θ sequence spaces.

• Korean Journal of Mathematics
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• 제32권1호
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• pp.109-120
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• 2024

The aim of this research is to describe lacunary ∆^m-statistically convergent sequences with respect to metrics on generalised metric spaces (g-metric spaces) and to look into the fundamental characteristics of this statistical form of convergence. Also, the relationship between strong summability and lacunary ∆^m-statistical convergence in g-metric space is established at the end.

• Korean Journal of Mathematics
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• 제29권2호
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• pp.211-225
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• 2021

In the present paper we introduce some sequence spaces over n-normed spaces defined by fractional difference operator and Musielak-Orlicz function 𝓜 = (𝕱_i). We also study some topological properties and prove some inclusion relations between these spaces.