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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Vydáno v:	Cumhuriyet Science Journal Ročník 44; číslo 4; s. 753 - 757
Hlavní autoři:	Belen, Cemal, Yıldırım, Mustafa
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Sivas Cumhuriyet Üniversitesi 28.12.2023
Témata:	compatible modulus function deferred statistical convergence strong deferred convergence uniformly integrable sequence
ISSN:	2587-2680
On-line přístup:	Získat plný text
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Popis
Shrnutí:	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