SOME REMARKS ON GENERALIZED SUMMABILITY USING DIFFERENCE OPERATORS ON NEUTROSOPHIC NORMED SPACES

For the $m$th difference operator ${\triangle }^m$ and the admissible ideal ${\mathcal{I}}\subseteq {\mathcal{P}} \left(\mathbb{N}\right)$, the purpose of this paper is to introduce generalized summability methods: ${\triangle }^m({\mathcal{I}}_{\mathcal{N}})-$convergence and ${\triangle }^m({\mathcal{I}}^*_{\mathcal{N}})-$convergence in neutrosophic normed spaces (briefly known as$\ NNS$). We develop some basics properties of these notions and find condition on ${\mathcal{I}}$ for which two methods of summability coincides. Finally, we define ${\triangle }^m({\mathcal{I}}_{\mathcal{N}})-$Cauchy sequences in $NNS\ $and obtain the Cauchy-convergence criteria in these spaces.