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

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...

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Bibliographic Details
Published in:	Cumhuriyet Science Journal Vol. 44; no. 4; pp. 753 - 757
Main Authors:	Belen, Cemal, Yıldırım, Mustafa
Format:	Journal Article
Language:	English
Published:	Sivas Cumhuriyet Üniversitesi 28.12.2023
Subjects:	compatible modulus function deferred statistical convergence strong deferred convergence uniformly integrable sequence
ISSN:	2587-2680
Online Access:	Get full text
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Summary:	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.
ISSN:	2587-2680
DOI:	10.17776/csj.1334082