I−lacunary summability function of order α

Savaş E.

Filomat, vol.31, no.1, pp.69-76, 2017 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 31 Issue: 1
  • Publication Date: 2017
  • Doi Number: 10.2298/fil1701069s
  • Journal Name: Filomat
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.69-76
  • Keywords: Filter, I-lacunary statistical convergence, I-statistical convergence of order α, Ideal, Nonnegative real-valued function
  • Uşak University Affiliated: No

Abstract

In this paper, we further generalize recently introduced summability methods in [23](where ideals of ℕ were used to extend certain important summability methods) and introduce new notions, namely, I−statistical convergence of order α, where 0 < α < 1 by taking nonnegative real-valued Lebesque measurable function in the interval (1, ∞). We mainly investigate their relationship and also make some observations about these classes. The study leaves a lot of interesting open problems.