Double Lacunary Statistical Convergence of Order \(\alpha\) in Topological Groups via Ideal

Ekrem Savas

doi:10.26713/cma.v9i3.781

Authors

Ekrem Savas Department of Mathematics, Usak University, Usak

DOI:

https://doi.org/10.26713/cma.v9i3.781

Keywords:

Double lacunary, Ideal double lacunary statistical convergence, Topological groups

Abstract

Recently, \(\mathcal{I}\)-lacunary double statistical convergence in topological groups is presented by Savas [31]. In this paper, we extend the concepts of \(\mathcal{I}\)-double statistical convergence and \(\mathcal{I}\)-double lacunary statistical convergence to the concepts of \(\mathcal{I}\)-double statistical convergence and \(\mathcal{I}\)-double lacunary statistical convergence of order \(\alpha\), \(0 <\alpha \leq 1\). We also investigate some inclusion relations between \(\mathcal{I}\)-double statistical of order \(\alpha\) and \(\mathcal{I}\)-double lacunary double statistical convergence of order \(\alpha\).

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