On I-lacunary statistical convergence of weight g of sequences of sets

Savaş E.

Filomat, vol.31, no.16, pp.5315-5322, 2017 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 31 Issue: 16
  • Publication Date: 2017
  • Doi Number: 10.2298/fil1716315s
  • Journal Name: Filomat
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.5315-5322
  • Keywords: I-lacunary statistical convergence, I-statistical convergence, Statistical convergence of weight g, Wijsman lacunary statistical convergence, Wijsman statistical convergence
  • Uşak University Affiliated: No

Abstract

In this paper, following a very recent and new approach of [1], we further generalize recently introduced summability methods in [13] and introduce new notions, namely, I-statistical convergence of weight 1 and I-lacunary statistical convergence of weight 1, where g: N → [0, ∞) is a function satisfying (Formula presented) and (Formula presented) as n → ∞, for sequences of sets. We mainly investigate their relationship and also make some observations about these classes. The study leaves a lot of interesting open problems.