On Deferred Statistical and Strong Deferred Cesàro Convergences of Sequences With Respect to A Modulus Function
Cemal Belen,
Mustafa Yıldırım
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.
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