On i-statistically pre-cauchy sequences

Das P., Savas E.

Taiwanese Journal of Mathematics, cilt.18, sa.1, ss.115-126, 2014 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 18 Sayı: 1
  • Basım Tarihi: 2014
  • Doi Numarası: 10.11650/tjm.18.2014.3157
  • Dergi Adı: Taiwanese Journal of Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.115-126
  • Anahtar Kelimeler: Filter, I- natural density, I-limit inferior, I-statistical convergence, I-statistical pre-cauchy condition, Ideal
  • Uşak Üniversitesi Adresli: Hayır

Özet

In this paper we continue our investigation of the recent summability notion of I-statistical convergence introduced in [8, 26] (where a new extension of the notion of natural density and statistical convergence was proposed using the notion of ideals of the set of positive integers N) and introduce the notion of I-statistically pre-Cauchy sequences in line of [3]. We mainly show that I-statistical convergence implies I-statistical pre-Cauchy condition and give certain sufficient conditions for the converse to be true.