@misc{10498/21970,
year = {2019},
month = {11},
url = {http://hdl.handle.net/10498/21970},
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.},
publisher = {SPRINGEROPEN},
keywords = {Statistical convergence},
keywords = {Strong Cesaro convergence},
keywords = {Modulus function},
keywords = {Uniformly bounded sequence},
title = {On statistical convergence and strong Cesàro convergence by moduli},
doi = {10.1186/s13660-019-2252-y},
author = {León Saavedra, Fernando and Listán García, María del Carmen and Pérez Fernández, Francisco Javier and Romero de la Rosa, María Pilar},
}