On statistical convergence and strong Cesàro convergence by moduli

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URI: http://hdl.handle.net/10498/21970
DOI: 10.1186/s13660-019-2252-y
ISSN: 1029-242X
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2019-11Department
MatemáticasSource
Journal of Inequalities and Applications volume 2019, Article number: 298 (2019)Abstract
In this paper we will establish a result by Connor, Khan and Orhan (Analysis 8:47–63,
1988; Publ. Math. (Debr.) 76:77–88, 2010) in the framework of the statistical
convergence and the strong Cesàro convergence defined by a modulus function f .
Namely, for every modulus function f , we will prove that a f -strongly Cesàro
convergent sequence is always f -statistically convergent and uniformly integrable.
The converse of this result is not true even for bounded sequences. We will
characterize analytically the modulus functions f for which the converse is true. We
will prove that these modulus functions are those for which the statistically
convergent sequences are f -statistically convergent, that is, we show that
Connor–Khan–Orhan’s result is sharp in this sense.
Subjects
Statistical convergence; Strong Cesaro convergence; Modulus function; Uniformly bounded sequenceCollections
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