RT Journal Article
T1 On statistical convergence and strong Cesaro convergence by moduli
A1 Leon-Saavedra, Fernando
A1 Listan-Garcia, M. del Carmen
A1 Perez Fernandez, Francisco Javier
A1 Romero de la Rosa, Maria Pilar
K1 Statistical convergence
K1 Strong Cesaro convergence
K1 Modulus function
K1 Uniformly bounded sequence
K1 Approximation theorems
K1 Korovkin
K1 Summability
K1 Sequences
K1 Spaces
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 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.
PB Springeropen
SN 1029-242X
YR 2019
FD 2019-11-14
LK http://hdl.handle.net/10668/19135
UL http://hdl.handle.net/10668/19135
LA en
DS RISalud
RD Apr 9, 2025