Tauberian theorems for statistically convergent double sequences
The authors consider two summability methods for real or complex double sequences \((x_{mn})\,.\) They mainly investigate the relation between statistical convergence and Cesàro \(C_{1,1}\)-conver\-gence and the relation of the two methods to convergence. They show that for bounded sequences Cesàro convergence is stronger than statistical convergence and furthermore that the condition \(| x_{mj}-x_{m,j-1}| \leq c/j\) together with the condition \(| x_{kn}-x_{k-1,n}| \leq c/k\) (uniformly in \(m,n\)) form a Tauberian condition from statistical convergence to convergence and from statistical convergence of the Cesàro mean to convergence. A related Tauberian theorem for the Cesàro method is well known.
scientific article; zbMATH DE number 5015634
scientific article