On statistical convergence and strong Cesàro convergence by moduli for double sequences

Abstract

AbstractA remarkable result on summability states that the statistical convergence and the strong Cesàro convergence are closely connected. Given a modulus functionf, we will establish that a double sequence that isf-strong Cesàro convergent is alwaysf-statistically convergent. The converse, in general, is false even for bounded sequences. However, we will characterize analytically the modulus functionsffor which the converse of this result remains true. The results of this paper adapt to several variables the results obtained in (León-Saavedra et al. in J. Inequal. Appl. 12:298, 2019).