On statistical convergence and strong Cesàro convergence by moduli

Journal of Inequalities and Applications

Research

Fernando León-Saavedra¹  María Pilar Romero de la Rosa¹  Francisco Javier Pérez Fernández²  M. del Carmen Listán-García² 

[1] Department of Mathematics, University of Cádiz, Jerez de la Frontera, Spain;Department of Mathematics, University of Cádiz, Puerto Real, Spain;

关键词: Statistical convergence;    Strong Cesàro convergence;    Modulus function;    Uniformly bounded sequence;   

DOI  :  10.1186/s13660-019-2252-y

 received in 2019-06-06, accepted in 2019-11-06,  发布年份 2019

来源: Springer

【 摘 要 】

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.

【 授权许可】

CC BY   
© The Author(s) 2019. corrected publication 2023

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