On Lacunary $\mathcal{I}_2^{\ast }$-Convergence and Lacunary $\mathcal{I}_2^{\ast }$-Cauchy Sequence

Year 2023, Volume: 6 Issue: 4, 188 - 195, 25.12.2023

Nimet Pancaroğlu Akın Erdinç Dündar

https://doi.org/10.33434/cams.1363596

Cited By: 1

Abstract

In the study conducted here, we have given some new concepts in summability. In this sense, firstly, we have given the concept of lacunary $\mathcal{I}_2^{\ast}$-convergence and we have investigated the relations between lacunary $\mathcal{I}_2$-convergence and lacunary $\mathcal{I}_2^{\ast}$-convergence. Also, we have given the concept of lacunary $\mathcal{I}_2^{\ast}$-Cauchy sequence and investigated the
relations between lacunary $\mathcal{I}_2$-Cauchy sequence and lacunary $\mathcal{I}_2^{\ast}$-Cauchy sequence.

Keywords

Double sequence, Ideal convergence, Ideal Cauchy sequence, Lacunary sequence

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