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On statistical convergence and strong Cesàro convergence by moduli.
- Source :
-
Journal of Inequalities & Applications . 11/14/2019, Vol. 2019 Issue 1, pN.PAG-N.PAG. 1p. - Publication Year :
- 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. [ABSTRACT FROM AUTHOR]
- Subjects :
- *SEQUENCE spaces
*MATHEMATICS
Subjects
Details
- Language :
- English
- ISSN :
- 10255834
- Volume :
- 2019
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Journal of Inequalities & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 139693744
- Full Text :
- https://doi.org/10.1186/s13660-019-2252-y