ON CERTAIN GENERALIZED MATRIX METHODS OF CONVERGENCE IN (ℓ)-GROUPS.

We introduce a convergence of weight g : N→[0,∞) where g(n)→∞ and n=g(n)↛0 with respect to a summability matrix method A for sequences (which generalizes the notion of A-convergence of order α; 0 < α ≤ 1 [BOCCUTO, A.-DAS, P.: On matrix methods of convergence of order (α) in (ℓ)-groups, Filomat 29 (2015), 2069-2077] in a (ℓ)-group. We prove some basic results including a Cauchy-type criterion. Finally a closedness result for the space of such convergent sequences is proved. [ABSTRACT FROM AUTHOR]