NEW NOTIONS ON IDEAL CONVERGENCE OF TRIPLE SEQUENCES IN NEUTROSOPHIC NORMED SPACES

NEW NOTIONS ON IDEAL CONVERGENCE OF TRIPLE SEQUENCES IN NEUTROSOPHIC NORMED SPACES

C. GRANADOS, C. CHOUDHURY

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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.

Keywords:Statistical convergence, ideal, filter, I-convergence, neutrosophic normed space, triple sequences.

AMS Subject Classification: 46S40, 03E72, 40A35.