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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 I3*-convergence of triple sequences in neutrosophic normed spaces mainly as a generalization of statistical con- vergence 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 3*-Cauchy sequence of triple sequences and show that the condition (AP3) plays a crucial role to study the interrelationship between them.
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