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.
$\mathcal{I}_2$-Cauchy Sequence $\mathcal{I}_2$-Convergence Double sequence Ideal Lacunary sequence
Primary Language | English |
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Subjects | Pure Mathematics (Other) |
Journal Section | Articles |
Authors | |
Early Pub Date | December 4, 2023 |
Publication Date | December 18, 2023 |
Submission Date | October 16, 2023 |
Acceptance Date | November 30, 2023 |
Published in Issue | Year 2023 |
Universal Journal of Mathematics and Applications
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