I-STATISTICAL CONVERGENCE IN PROBABILISTIC NORMED SPACES


Savas E., GÜRDAL M.

UNIVERSITY POLITEHNICA OF BUCHAREST SCIENTIFIC BULLETIN-SERIES A-APPLIED MATHEMATICS AND PHYSICS, vol.77, no.4, pp.195-204, 2015 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 77 Issue: 4
  • Publication Date: 2015
  • Title of Journal : UNIVERSITY POLITEHNICA OF BUCHAREST SCIENTIFIC BULLETIN-SERIES A-APPLIED MATHEMATICS AND PHYSICS
  • Page Numbers: pp.195-204

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.