On I-lacunary statistical convergence of order α for sequences of sets

Savaş E.

Filomat, vol.29, no.6, pp.1223-1229, 2015 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 29 Issue: 6
  • Publication Date: 2015
  • Doi Number: 10.2298/fil1506223s
  • Journal Name: Filomat
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1223-1229
  • Keywords: I-lacunary statistical convergence, I-statistical convergence, Statistical convergence of order α, Wijsman lacunary statistical convergence, Wijsman statistical convergence
  • Uşak University Affiliated: No

Abstract

In this paper, following a very recent and new approach of [1] and [2] we further generalize recently introduced summability methods in [11] and introduce new notions, namely, I-statistical convergence of order α and I-lacunary statistical convergence of order α, where 0 < α ≤ 1 for sequences of sets. We mainly study their relationship and also make some observations about these classes and in the way try to give a proof of theorem which is not proved in [31]. The study leaves a lot of interesting open problems.