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

Print ISSN: 2319-1023 | Online ISSN: 2582-5461 | Total Downloads : 65

Abstract

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.

Keywords and Phrases

Neutrosophic normed spaces, statistical convergence, statistical Cauchy, ${\mathcal{I}}-$convergence and ${\mathcal{I}}-$Cauchy sequences.

A.M.S. subject classification

46S40, 11B39, 03E72, 40G15.

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