On ideal invariant convergence of double sequences and some properties

Dündar, Erdinç, Ulusu, Uǧur and Nuray, Fatih

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creative_2018_27_2_161_169

DOI: https://doi.org/10.37193/CMI.2018.02.08

Issue no: Vol 27/2018 no. 2 Tags: double sequence, $\mathcal{I}$-convergence, invariant convergence, $\mathcal{I}$-Cauchy sequence

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In this paper, we study the concepts of invariant convergence, $p$ -strongly invariant convergence $([V_{\sigma}^2]_{p})$ , $\mathcal{I}_2$ -invariant convergence ( $\mathcal{I}^{\sigma}_{2}$ ), $\mathcal{I}^{*}_2$ -invariant convergence ( $\mathcal{I}^{{\sigma}*}_{2}$ ) of double sequences and investigate the relationships among invariant convergence, $[V_{\sigma}^2]_{p}$ , $\mathcal{I}^{\sigma}_{2}$ and $\mathcal{I}^{{\sigma}*}_{2}$ . Also, we introduce the concepts of $\mathcal{I}^{\sigma}_{2}$ -Cauchy double sequence and $\mathcal{I}^{{\sigma}*}_{2}$ -Cauchy double sequence.