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

Year 2023, Volume: 6 Issue: 4, 155 - 161, 18.12.2023

Erdinç Dündar , Nimet Pancaroğlu Akın , Esra Gülle

https://doi.org/10.32323/ujma.1376849

Cited By: 1

Abstract

In the study conducted here, we have given some new concepts in summability theory. In this sense, firstly, using the lacunary sequence we have given the concept of strongly $\mathcal{I}_{\theta_2}^{\ast}$-convergence and we have examined the relations between $\mathcal{I}_{\theta_2}^{\ast}$-convergence and strongly $\mathcal{I}_{\theta_2}^{\ast}$-convergence and also between strongly $\mathcal{I}_{\theta_2}$-convergence and strongly $\mathcal{I}_{\theta_2}^{\ast}$-convergence. Also, using the lacunary sequence we have given the concept of strongly $\mathcal{I}_{\theta_2}^{\ast}$-Cauchy sequence and examined the relations between strongly $\mathcal{I}_{\theta_2}$-Cauchy sequence and strongly $\mathcal{I}_{\theta_2}^{\ast}$-Cauchy sequence.

Keywords

$\mathcal{I}_2$-Cauchy Sequence, $\mathcal{I}_2$-Convergence, Double sequence, Ideal, Lacunary sequence

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