Generalized neutrosophic ideal convergent sequence spaces

Volume 30, Issue 4, pp 332--339 http://dx.doi.org/10.22436/jmcs.030.04.03

Publication Date: February 10, 2023 Submission Date: September 15, 2022 Revision Date: October 06, 2022 Accteptance Date: January 14, 2023

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Authors

M. Ahmad - Department of Mathematics , Presidency University, School of Engineering, Coimbatore- 641 407, Bangalore, 560064, India . M. I. Idrisi - Department of Mathematics, University Institute of Sciences, Chandigarh University, 140413, India. A. K. Sirohi - School of Computational and Integrative Sciences, Jawaharlal Nehru University, New Delhi, 110067, India.

Abstract

Kostyrko et al. initiated the concept of ideal convergence in [P. Kostyrko, T. Šalát, W. Wilczyński, Real Anal. Exchange, \(\bf 26\) (2000), 669--686]. The purpose of this paper is to introduce and define spaces of the neutrosophic convergent sequence via ideal, namely \(^{I}\mathcal{S}_{\mathcal{M}}\) and \(^{I}\mathcal{S}_{\mathcal{M}_{0}}\). We prove that new spaces are linear and Hausdorff topological spaces. Further, we examine the relation between \(I\)-Cauchy and \(I\)-convergent sequences and show that every separable space \(^{I}\mathcal{S}_{\mathcal{M}}\) is second countable. Moreover, we prove that the space \(^{I}\mathcal{S}_{\mathcal{M}}\) is complete.

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Keywords

• Ideal
• filter
• \(I\)-convergence
• \(I\)-Cauchy
• \(t\)-norm
• \(t\)-conorm
• neutrosophic normed space

MSC

•  46S40
•  11B39
•  03E72
•  40G15

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