• Journal of applied mathematics & informatics
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• v.39 no.3_4
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• pp.277-294
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• 2021

In this paper, we introduce the notions of Wijsman regularly invariant convergence types, Wijsman regularly (${\mathcal{I}}_{\sigma}$, ${\mathcal{I}}^{\sigma}_2$)-convergence, Wijsman regularly (${\mathcal{I}}^*_{\sigma}$, ${\mathcal{I}}^{{\sigma}*}_2$)-convergence, Wijsman regularly (${\mathcal{I}}_{\sigma}$, ${\mathcal{I}}^{\sigma}_2$) -Cauchy double sequence and Wijsman regularly (${\mathcal{I}}^*_{\sigma}$, ${\mathcal{I}}^{{\sigma}*}_2$)-Cauchy double sequence of sets. Also, we investigate the relationships among this new notions.

• Honam Mathematical Journal
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• v.42 no.2
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• pp.345-358
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• 2020

In this paper, we study the concepts of Wijsman lacunary invariant convergence, Wijsman lacunary invariant statistical convergence, Wijsman lacunary ${\mathcal{I}}_2$-invariant convergence (${\mathcal{I}}^{{\sigma}{\theta}}_{W_2}$), Wijsman lacunary ${\mathcal{I}}^*_2$-invariant convergence (${\mathcal{I}}^{\ast}^{{\sigma}{\theta}}_{W_2}$), Wijsman p-strongly lacunary invariant convergence ([W₂N_σθ]_p) of double sequence of sets and investigate the relationships among Wijsman lacunary invariant convergence, [W₂N_σθ]_p, ${\mathcal{I}}^{{\sigma}{\theta}}_{W_2}$ and ${\mathcal{I}}^{\ast}^{{\sigma}{\theta}}_{W_2}$. Also, we introduce the concepts of ${\mathcal{I}}^{{\sigma}{\theta}}_{W_2}$-Cauchy double sequence and ${\mathcal{I}}^{\ast}^{{\sigma}{\theta}}_{W_2}$-Cauchy double sequence of sets.

• Journal of applied mathematics & informatics
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• v.40 no.1_2
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• pp.327-339
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• 2022

In this paper, we introduce arithmetic ${\mathcal{I}}$-statistically convergent sequence space $A{\mathcal{I}}SC$, ${\mathcal{I}}$-lacunary arithmetic statistically convergent sequence space $A{\mathcal{I}}SC_{\theta}$, strongly ${\mathcal{I}}$-lacunary arithmetic convergent sequence space $AN_{\theta}[{\mathcal{I}}]$ and prove some inclusion relations between these spaces. Futhermore, we give ${\mathcal{I}}$-lacunary arithmetic statistical continuity. Finally, we define ${\mathcal{I}}$-Cesàro arithmetic summability, strongly ${\mathcal{I}}$-Cesàro arithmetic summability. Also, we investigate the relationship between the concepts of strongly ${\mathcal{I}}$-Cesàro arithmetic summability, strongly ${\mathcal{I}}$-lacunary arithmetic summability and arithmetic ${\mathcal{I}}$ -statistically convergence.

• Journal of Applied and Pure Mathematics
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• v.4 no.1_2
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• pp.37-50
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• 2022

In this article we define and study the notions of $\mathcal{I}$-convergence and $\mathcal{I}$-Cauchy of triple sequences in the topology induced by random 2-normed spaces and prove some theorems based on them.

• 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.

• Honam Mathematical Journal
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• v.43 no.2
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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.