On I-statistical and I-lacunary statistical convergence of order α

Das P., Savas E.

Bulletin of the Iranian Mathematical Society, cilt.40, sa.2, ss.459-472, 2014 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 40 Sayı: 2
  • Basım Tarihi: 2014
  • Dergi Adı: Bulletin of the Iranian Mathematical Society
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.459-472
  • Anahtar Kelimeler: Closed subspace, Filter, I- lacunary statistical convergence of order α, I-statistical convergence of order α, Ideal
  • Uşak Üniversitesi Adresli: Hayır

Özet

In this paper, following a very recent and new approach, we further generalize recently introduced summability methods, namely, I-statistical convergence and I-lacunary statistical convergence (which extend the important summability methods, statistical convergence and lacunary statistical convergence using ideals of N) and introduce the notions of I-statistical convergence of order α and I-lacunary statistical convergence of order α, where 0 < α < 1. We mainly investigate their relationship and also make some observations about these classes and in the way try to give an answer to an open problem posed By Das, Savas and Ghosal in 2011. The study leaves a lot of interesting open problems. © 2014 Iranian Mathematical Society.