Lacunary I-invariant convergence
Abstract
In this study, firstly, we introduce the notion of lacunary invariant uniform density of any subset E of the set N (the set of all natural numbers). Then, as associated with this notion, we give the definition of lacunary I_σ-convergence for real sequences. Furthermore, we examine relations between this new type convergence notion and the notions of lacunary invariant summability, lacunary strongly q-invariant summability and lacunary σ-statistical convergence which are studied in this area before. Finally, introducing the notions of lacunary I_σ^*-convergence and I_σ-Cauchy sequence, we give the relations between these notions and the notion of lacunary I_σ-convergence.
Keywords
Lacunary sequence, I-convergence, Invariant convergence, Statistical convergence, I-Cauchy sequence
Supporting Institution
The Scientific Research Project Fund of Afyon Kocatepe University
Project Number
16.KARİYER.62
Thanks
We would like to thank "The Scientific Research Project Fund of Afyon Kocatepe University" for its support with this project, project number 16.KARİYER.62.
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