On matrix methods of convergence of order \alpha in (l)-groups

Abstract

Taking inspiration from [Bhunia et al, Acta Math. Hungar, 2012] we introduce a concept of convergence of order\alpha , with
0 < \alpha < 1, with respect to a summability matrix method A for sequences (which gen-
eralizes the notion of statistical convergence of order \alpha, taking values in (l)-groups.
Some main properties and dierences with the classical A-convergence are investigated.
A Cauchy-type criterion and a closedness result for the space of convergent sequences
according our notion is proved.