On i-statistically pre-cauchy sequences

Das P., Savas E.

Taiwanese Journal of Mathematics, vol.18, no.1, pp.115-126, 2014 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 18 Issue: 1
  • Publication Date: 2014
  • Doi Number: 10.11650/tjm.18.2014.3157
  • Journal Name: Taiwanese Journal of Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.115-126
  • Keywords: Filter, I- natural density, I-limit inferior, I-statistical convergence, I-statistical pre-cauchy condition, Ideal
  • Uşak University Affiliated: No

Abstract

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.