Some further remarks on ideal summability in 2-normed spaces

Abstract

Very recently ideals were used to study the summability of sequences in 2-normed spaces by Gurdal and Acik (2008) [18], Gurdal and Pehlivan (2004) [19] and Sahiner et al. (2007) [11], who investigated some convergence and Cauchy conditions (namely I -convergence and I ∗ -convergence and Cauchy conditions). In this work we make some further investigations along these lines which provide answers to two important questions regarding I -Cauchy and I ∗ -Cauchy sequences which were left unanswered. We then introduce new concepts of I -divergence and I ∗ -divergence in 2-normed spaces and study some of their properties.