Some further results on I-Cauchy sequences and condition (AP)I

In this paper we provide answers to two important questions regarding I and I -Cauchy sequences introduced and studied by Nabiev et al. (2007) [9] which were left unanswered. We then introduce the ideas of I and I -divergent sequences in a metric space and study their certain properties. Our investigation strengthens and reconfirms importance of condition (AP) in the study of summability through ideals.