I-statistical convergence in probabilistic normed spaces

Savas E., GÜRDAL M.

UPB Scientific Bulletin, Series A: Applied Mathematics and Physics, cilt.77, sa.4, ss.195-204, 2015 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 77 Sayı: 4
  • Basım Tarihi: 2015
  • Dergi Adı: UPB Scientific Bulletin, Series A: Applied Mathematics and Physics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.195-204
  • Anahtar Kelimeler: Double sequence, Ideal, t-norm, probabilistic normed space, I-statistical convergence, I-lacunary statistical convergence
  • İstanbul Ticaret Üniversitesi Adresli: Evet

Özet

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.