On Deferred Statistical and Strong Deferred Cesàro Convergences of Sequences With Respect to A Modulus Function

Cemal Belen; Mustafa Yıldırım

doi:10.17776/csj.1334082

EN

On Deferred Statistical and Strong Deferred Cesàro Convergences of Sequences With Respect to A Modulus Function

Abstract

Let f be any modulus function. We prove that the classes of strongly deferred Cesàro convergent sequences defined by f and deferred statistical convergent sequences are equivalent if the sequence is f-deferred uniformly integrable. Some converse inclusions are obtained when the modulus function f is compatible. Finally, for any compatible modulus f, we prove that any sequence is f-strongly deferred Cesàro convergent if and ony if it is deferred f-statistically convergent and deferred uniformly integrable.

Keywords

Deferred statistical convergence, Strong deferred convergence, Uniformly integrable sequence, Compatible modulus function.

References

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Details

Primary Language

English

Subjects

Theoretical and Applied Mechanics in Mathematics

Journal Section

Research Article

Authors

Cemal Belen
0000-0002-8832-1524
Türkiye

Mustafa Yıldırım ^*
0000-0002-8880-5457
Türkiye

Publication Date

December 28, 2023

Submission Date

July 28, 2023

Acceptance Date

November 2, 2023

Published in Issue

Year 2023 Volume: 44 Number: 4

DOI

https://doi.org/10.17776/csj.1334082

IZ

https://izlik.org/JA93PP36MC

APA

Belen, C., & Yıldırım, M. (2023). On Deferred Statistical and Strong Deferred Cesàro Convergences of Sequences With Respect to A Modulus Function. Cumhuriyet Science Journal, 44(4), 753-757. https://doi.org/10.17776/csj.1334082

AMA

1.Belen C, Yıldırım M. On Deferred Statistical and Strong Deferred Cesàro Convergences of Sequences With Respect to A Modulus Function. CSJ. 2023;44(4):753-757. doi:10.17776/csj.1334082

Chicago

Belen, Cemal, and Mustafa Yıldırım. 2023. “On Deferred Statistical and Strong Deferred Cesàro Convergences of Sequences With Respect to A Modulus Function”. Cumhuriyet Science Journal 44 (4): 753-57. https://doi.org/10.17776/csj.1334082.

EndNote

Belen C, Yıldırım M (December 1, 2023) On Deferred Statistical and Strong Deferred Cesàro Convergences of Sequences With Respect to A Modulus Function. Cumhuriyet Science Journal 44 4 753–757.

IEEE

[1]C. Belen and M. Yıldırım, “On Deferred Statistical and Strong Deferred Cesàro Convergences of Sequences With Respect to A Modulus Function”, CSJ, vol. 44, no. 4, pp. 753–757, Dec. 2023, doi: 10.17776/csj.1334082.

ISNAD

Belen, Cemal - Yıldırım, Mustafa. “On Deferred Statistical and Strong Deferred Cesàro Convergences of Sequences With Respect to A Modulus Function”. Cumhuriyet Science Journal 44/4 (December 1, 2023): 753-757. https://doi.org/10.17776/csj.1334082.

JAMA

1.Belen C, Yıldırım M. On Deferred Statistical and Strong Deferred Cesàro Convergences of Sequences With Respect to A Modulus Function. CSJ. 2023;44:753–757.

MLA

Belen, Cemal, and Mustafa Yıldırım. “On Deferred Statistical and Strong Deferred Cesàro Convergences of Sequences With Respect to A Modulus Function”. Cumhuriyet Science Journal, vol. 44, no. 4, Dec. 2023, pp. 753-7, doi:10.17776/csj.1334082.

Vancouver

1.Cemal Belen, Mustafa Yıldırım. On Deferred Statistical and Strong Deferred Cesàro Convergences of Sequences With Respect to A Modulus Function. CSJ. 2023 Dec. 1;44(4):753-7. doi:10.17776/csj.1334082

Cited By

Modulated convergence: a deferred approach

Demonstratio Mathematica

https://doi.org/10.1515/dema-2025-0185

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