%0 Journal Article 
%A León Saavedra, Fernando
%A Listán García, María del Carmen
%A Pérez Fernández, Francisco Javier
%A Romero de la Rosa, María Pilar
%T On statistical convergence and strong Cesàro convergence by moduli
%D 2019
%@ 1029-242X
%U http://hdl.handle.net/10498/21970
%X 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.
%K Statistical convergence
%K Strong Cesaro convergence
%K Modulus function
%K Uniformly bounded sequence
%~ Universidad de Cádiz