RT journal article
T1 On statistical convergence and strong Cesàro convergence by moduli
A1 León Saavedra, Fernando
A1 Listán García, María del Carmen
A1 Pérez Fernández, Francisco Javier
A1 Romero de la Rosa, María Pilar
A2 Matemáticas
K1 Statistical convergence
K1 Strong Cesaro convergence
K1 Modulus function
K1 Uniformly bounded sequence
AB 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 statisticalconvergence and the strong Cesàro convergence defined by a modulus function f .Namely, for every modulus function f , we will prove that a f -strongly Cesàroconvergent sequence is always f -statistically convergent and uniformly integrable.The converse of this result is not true even for bounded sequences. We willcharacterize analytically the modulus functions f for which the converse is true. Wewill prove that these modulus functions are those for which the statisticallyconvergent sequences are f -statistically convergent, that is, we show thatConnor–Khan–Orhan’s result is sharp in this sense.
PB SPRINGEROPEN
SN 1029-242X
YR 2019
FD 2019-11
LK http://hdl.handle.net/10498/21970
UL http://hdl.handle.net/10498/21970
LA eng
DS Repositorio Institucional de la Universidad de Cádiz
RD 10-may-2026