Mathematics and Statistics Vol. 11(5), pp. 845 - 855
DOI: 10.13189/ms.2023.110512
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Convergence of the Jordan Neutrosophic Ideal in Neutrosophic Normed Spaces

R. Muthuraj ¹, K. Nachammal ¹, M. Jeyaraman ^2,*, D. Poovaragavan ^3
1 Department of Mathematics, H.H. The Rajah’s College, Pudukkottai, Affiliated to Bharathidasan University, India
² Department of Mathematics, Raja Doraisingam Govt. Arts College, Sivagangai, Affiliated to Alagappa University, India
³ Department of Mathematics, Government Arts College for Women, Sivagangai, Affiliated to Alagappa University, India

ABSTRACT

In the context of the Neutrosophic Norm, the essay explores the challenge of constructing precise sequence spaces whose elements' convergence is a generalised form of the Cauchy convergence. It has proven to be a crucial tool, opening the door to the theory of functions and the law of large numbers applications. Numerous authors, including those who investigated the Euler totient matrix operator, have studied the strategy for building new sequence spaces that are specified as the domain of matrix operators. Recently, the Jordan totient function generalised the Euler totient function . In the context of neutrosophic Norm spaces, we establish some sequence spaces, specifically , and as a domain of the triangular Jordan totient matrix operator, and investigate the ideal convergence of these sequences. These concepts serve as an introduction to a new sort of convergence that Fast and Steinhaus presented as more general than normal convergence and statistical convergence. According to Kostyrko et al., this form is known as ideal convergence. In order to arrive at a finite limit, the Jordan totient operator, an infinite matrix operator, is used. We also construct a number of inclusion connections between the spaces as we explain various topological and algebraic properties. The Jordan totient operator, an infinite matrix operator, is used to accomplish the task of reaching a finite limit. As we discuss various topological and algebraic features, we also create several inclusion relations between the spaces.

KEYWORDS
Jordan -convergence, Compactness, Completeness, Hausdorff, Neutrosophic Sets

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] R. Muthuraj , K. Nachammal , M. Jeyaraman , D. Poovaragavan , "Convergence of the Jordan Neutrosophic Ideal in Neutrosophic Normed Spaces," Mathematics and Statistics, Vol. 11, No. 5, pp. 845 - 855, 2023. DOI: 10.13189/ms.2023.110512.

(b). APA Format:
R. Muthuraj , K. Nachammal , M. Jeyaraman , D. Poovaragavan (2023). Convergence of the Jordan Neutrosophic Ideal in Neutrosophic Normed Spaces. Mathematics and Statistics, 11(5), 845 - 855. DOI: 10.13189/ms.2023.110512.