On lacunary \(\mathcal{I}\)-invariant arithmetic convergence
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https://doi.org/10.26637/mjm0902/001Abstract
In this study, we investigate the notion of lacunary \(\mathcal{I}_{\sigma }\) arithmetic convergence for real sequences and examine relations between this new type convergence notion and the notions of lacunary invariant arithmetic summability, lacunary strongly \(q\)-invariant arithmetic summability and lacunary \(\sigma\)-statistical arithmetic convergence which are defined in this study. Finally, giving the notions of lacunary \(\mathcal{I}_{\sigma }\) arithmetic statistically convergence, lacunary strongly \(\mathcal{I}_{\sigma }\) arithmetic summability, we prove the inclusion relation between them.
Keywords:
Lacunary sequence, statistical convergence, invariant, arithmetic convergenceMathematics Subject Classification:
40A05 , 40A99 , 46A70 , 46A99- Pages: 1-11
- Date Published: 01-04-2021
- Vol. 9 No. 02 (2021): Malaya Journal of Matematik (MJM)
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