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- Title
On statistical convergence and strong Cesàro convergence by moduli.
- Authors
León-Saavedra, Fernando; Listán-García, M. del Carmen; Pérez Fernández, Francisco Javier; Romero de la Rosa, María Pilar
- 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
SEQUENCE spaces; MATHEMATICS
- Publication
Journal of Inequalities & Applications, 2019, Vol 2019, Issue 1, pN.PAG
- ISSN
1025-5834
- Publication type
Article
- DOI
10.1186/s13660-019-2252-y