ON $I$-STATISTICALLY PRE-CAUCHY SEQUENCES

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 $\mathbb{N}$) 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.