I−lacunary summability function of order α
Filomat, vol.31, no.1, pp.69-76, 2017 (SCI-Expanded, Scopus)
- 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.