Lacunary Arithmetic Statistical Convergence

A lacunary sequence is an increasing integer sequence θ = ( k r ) such that k r - k r - 1 → ∞ as r → ∞ . In this article, we introduce arithmetic statistically convergent sequence space ASC and lacunary arithmetic statistically convergent sequence space A S C θ and study some inclusion properties be...

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Bibliographic Details
Published in:National Academy science letters 2020-11, Vol.43 (6), p.547-551
Main Authors: Yaying, Taja, Hazarika, Bipan
Format: Article
Language:English
Subjects:
Arithmetic
Convergence
History of Science
Humanities and Social Sciences
Mathematics
multidisciplinary
Science
Science (multidisciplinary)
Short Communication
Statistics
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Summary:A lacunary sequence is an increasing integer sequence θ = ( k r ) such that k r - k r - 1 → ∞ as r → ∞ . In this article, we introduce arithmetic statistically convergent sequence space ASC and lacunary arithmetic statistically convergent sequence space A S C θ and study some inclusion properties between the two spaces. Finally, we introduce lacunary arithmetic statistical continuity and establish some interesting results.
ISSN:0250-541X
2250-1754
DOI:10.1007/s40009-020-00910-6