On certain generalized matrix methods of convergence in (ℓ)-groups

Abstract

Abstract 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.