• 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.

• Journal of Applied and Pure Mathematics
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• v.5 no.3_4
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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.