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

Erdinç Dündar; Nimet Pancaroğlu Akın; Esra Gülle

doi:10.32323/ujma.1376849

EN

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

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

References

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Details

Primary Language

English

Subjects

Pure Mathematics (Other)

Journal Section

Research Article

Authors

Erdinç Dündar ^*
0000-0002-0545-7486
Türkiye

Nimet Pancaroğlu Akın
0000-0003-4661-5388
Türkiye

Esra Gülle
0000-0001-5575-2937
Türkiye

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 Volume: 6 Number: 4

DOI

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

IZ

https://izlik.org/JA67UW22MD

APA

Dündar, E., Pancaroğlu Akın, N., & Gülle, E. (2023). On Strongly Lacunary $\mathcal{I}_2^{\ast }$-Convergence and Strongly Lacunary $\mathcal{I}_2^{\ast }$-Cauchy Sequence. Universal Journal of Mathematics and Applications, 6(4), 155-161. https://doi.org/10.32323/ujma.1376849

AMA

1.Dündar E, Pancaroğlu Akın N, Gülle E. On Strongly Lacunary $\mathcal{I}_2^{\ast }$-Convergence and Strongly Lacunary $\mathcal{I}_2^{\ast }$-Cauchy Sequence. Univ. J. Math. Appl. 2023;6(4):155-161. doi:10.32323/ujma.1376849

Chicago

Dündar, Erdinç, Nimet Pancaroğlu Akın, and Esra Gülle. 2023. “On Strongly Lacunary $\mathcal{I}_2^{\ast }$-Convergence and Strongly Lacunary $\mathcal{I}_2^{\ast }$-Cauchy Sequence”. Universal Journal of Mathematics and Applications 6 (4): 155-61. https://doi.org/10.32323/ujma.1376849.

EndNote

Dündar E, Pancaroğlu Akın N, Gülle E (December 1, 2023) On Strongly Lacunary $\mathcal{I}_2^{\ast }$-Convergence and Strongly Lacunary $\mathcal{I}_2^{\ast }$-Cauchy Sequence. Universal Journal of Mathematics and Applications 6 4 155–161.

IEEE

[1]E. Dündar, N. Pancaroğlu Akın, and E. Gülle, “On Strongly Lacunary $\mathcal{I}_2^{\ast }$-Convergence and Strongly Lacunary $\mathcal{I}_2^{\ast }$-Cauchy Sequence”, Univ. J. Math. Appl., vol. 6, no. 4, pp. 155–161, Dec. 2023, doi: 10.32323/ujma.1376849.

ISNAD

Dündar, Erdinç - Pancaroğlu Akın, Nimet - Gülle, Esra. “On Strongly Lacunary $\mathcal{I}_2^{\ast }$-Convergence and Strongly Lacunary $\mathcal{I}_2^{\ast }$-Cauchy Sequence”. Universal Journal of Mathematics and Applications 6/4 (December 1, 2023): 155-161. https://doi.org/10.32323/ujma.1376849.

JAMA

1.Dündar E, Pancaroğlu Akın N, Gülle E. On Strongly Lacunary $\mathcal{I}_2^{\ast }$-Convergence and Strongly Lacunary $\mathcal{I}_2^{\ast }$-Cauchy Sequence. Univ. J. Math. Appl. 2023;6:155–161.

MLA

Dündar, Erdinç, et al. “On Strongly Lacunary $\mathcal{I}_2^{\ast }$-Convergence and Strongly Lacunary $\mathcal{I}_2^{\ast }$-Cauchy Sequence”. Universal Journal of Mathematics and Applications, vol. 6, no. 4, Dec. 2023, pp. 155-61, doi:10.32323/ujma.1376849.

Vancouver

1.Erdinç Dündar, Nimet Pancaroğlu Akın, Esra Gülle. On Strongly Lacunary $\mathcal{I}_2^{\ast }$-Convergence and Strongly Lacunary $\mathcal{I}_2^{\ast }$-Cauchy Sequence. Univ. J. Math. Appl. 2023 Dec. 1;6(4):155-61. doi:10.32323/ujma.1376849