I-statistical convergence in probabilistic normed spaces

Savas E., GÜRDAL M.

UPB Scientific Bulletin, Series A: Applied Mathematics and Physics, vol.77, no.4, pp.195-204, 2015 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 77 Issue: 4
  • Publication Date: 2015
  • Journal Name: UPB Scientific Bulletin, Series A: Applied Mathematics and Physics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.195-204
  • Keywords: Double sequence, I-lacunary statistical convergence, I-statistical convergence, Ideal, Probabilistic normed space, T -norm
  • Uşak University Affiliated: No

Abstract

In this paper, we introduce a new type of summability notion, namely, I - statistical convergence and I -lacunary statistical convergence for double sequences in probabilistic normed space, which is a natural generalization of the notion of natural density, statistical convergence and lacunary statistical convergence using the notion of ideals of the set of positive integers N. In this context, we investigate their relationship, and make some observations about these classes using the tools of probabilistic normed space.