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

In this paper we provide answers to two important questions regarding II and I∗I∗-Cauchy sequences introduced and studied by Nabiev et al. (2007) [9] which were left unanswered. We then introduce the ideas of II and I∗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.