New notions on ideal convergence of triple sequences in neutrosophic normed spaces

Abstract

The usual convergence of sequences has many generalizations with the aim of providing deeper insights into the summability theory. In this paper, following a very recent and new approach, we introduce the notion of I3 and I*3?convergence of triple sequences in neutrosophic normed spaces mainly as a generalization of statistical convergence of triple sequences. We investigate a few fundamental properties and study the relationship between the two notions. We also introduce and investigate the concept of I3 and I*3?Cauchy sequence of triple sequences and show that the condition (AP3) plays a crucial role to study the interrelationship between them.