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

Abstract

AbstractWe introduce a convergence of weightg: ℕ → [0, ∞) whereg(n) → ∞ andn/g(n) ↛ 0 with respect to a summability matrix methodAfor sequences (which generalizes the notion ofA-convergence of orderα, 0 <α≤ 1 [BOCCUTO, A.—DAS, P.:On matrix methods of convergence of order(α)in(ℓ)-groups, Filomat29(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.