Certain aspects of $\mathcal{I}$-lacunary arithmetic statistical convergence

다국어 초록 (Multilingual Abstract)

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, $\mathcal{I}$-Ces\`{a}ro arithmetic summable and strongly $\mathcal{I}$-Ces\`{a}ro arithmetic summable using weighted density via Orlicz function $\widetilde{\phi}$. 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.