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

Year 2024, Volume: 12 Issue: 1, 20 - 27, 28.01.2024

Nimet Pancaroğlu Akın , Erdinç Dündar

https://doi.org/10.36753/mathenot.1330281

Abstract

In this paper, we defined the concepts of lacunary $\mathcal{I}^{\ast}$-convergence and strongly lacunary $\mathcal{I}^{\ast}$-convergence. We investigated the relations between strongly lacunary $\mathcal{I}$-convergence and strongly lacunary $\mathcal{I}^{\ast}$-convergence. Also, we defined the concept of strongly lacunary $\mathcal{I}^{\ast}$-Cauchy sequence and investigated the relations between strongly lacunary $\mathcal{I}$-Cauchy sequence and strongly lacunary $\mathcal{I}^{\ast}$-Cauchy sequence.

Keywords

Ideal, Lacunary sequence, $\mathcal{I}$-Convergence, $\mathcal{I}$-Cauchy Sequence

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