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Lacunary Arithmetic Statistical Convergence

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Abstract

A lacunary sequence is an increasing integer sequence \(\theta =(k_r)\) such that \(k_r-k_{r-1}\rightarrow \infty\) as \(r\rightarrow \infty .\) In this article, we introduce arithmetic statistically convergent sequence space ASC and lacunary arithmetic statistically convergent sequence space \(ASC_{\theta }\) and study some inclusion properties between the two spaces. Finally, we introduce lacunary arithmetic statistical continuity and establish some interesting results.

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Correspondence to Bipan Hazarika.

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Yaying, T., Hazarika, B. Lacunary Arithmetic Statistical Convergence. Natl. Acad. Sci. Lett. 43, 547–551 (2020). https://doi.org/10.1007/s40009-020-00910-6

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  • DOI: https://doi.org/10.1007/s40009-020-00910-6

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