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

Das P., Savas E.

Mathematica Slovaca, vol.67, no.4, pp.929-938, 2017 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 67 Issue: 4
  • Publication Date: 2017
  • Doi Number: 10.1515/ms-2017-0021
  • Journal Name: Mathematica Slovaca
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.929-938
  • Keywords: (ℓ)-group, A density of weight g, Ag-convergence, summability matrix
  • Uşak University Affiliated: No

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.