ON I-STATISTICALLY PRE-CAUCHY SEQUENCES

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.