%0 Journal Article
%A Leon-Saavedra, Fernando
%A Listan-Garcia, M. del Carmen
%A Perez Fernandez, Francisco Javier
%A Romero de la Rosa, Maria Pilar
%T On statistical convergence and strong Cesaro convergence by moduli
%D 2019
%@ 1029-242X
%U http://hdl.handle.net/10668/19135
%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 Cesaro convergence defined by a modulus function f. Namely, for every modulus function f, we will prove that a f-strongly Cesaro 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
%K Approximation theorems
%K Korovkin
%K Summability
%K Sequences
%K Spaces
%~