Journal of Applied and Pure Mathematics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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CERTAIN ASPECTS OF ${\mathcal{I}}$-LACUNARY ARITHMETIC STATISTICAL CONVERGENCE

  • MEHMET GURDAL (Department of Mathematics, Suleyman Demirel University)
  • Received : 2023.03.21
  • Accepted : 2023.05.21
  • Published : 2023.07.30
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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, ${\mathcal{I}}$-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.

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References

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