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

Ekrem Savas

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 \(\alpha\).

Keywords


Double lacunary; Ideal double lacunary statistical convergence; Topological groups

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References


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DOI: http://dx.doi.org/10.26713%2Fcma.v9i3.781

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