Continuous and bounded linear operators in neutrosophic normed spaces

Article type: Research Article

Authors: Khan, Vakeel A.^a | Esi, Ayhan^{b; *} | Ahmad, Mobeen^a | Daud Khan, Mohammad^a

Affiliations: [a] Department of Mathematics, Aligarh Muslim University, Aligarh, India | [b] Basic Engineering Sciences Department, Malatya Turgut Ozal University, Malatya, Turkey

Correspondence: [*] Corresponding author. Ayhan Esi, Basic Engineering Sciences Department, Malatya Turgut Zal Universitesi, Malatya, Turkey. E-mail: [email protected].

Abstract: In this article, we show that the addition and scalar multiplication in neutrosophic normed spaces are continuous. The neutrosophic boundedness and continuity of linear operators between neutrosophic normed spaces are examined. Moreover, we analyzed that the set of all neutrosophic continuous linear operators and the set of all neutrosophic bounded linear operators from neutrosophic normed spaces into another are vector spaces.

Keywords: Bounded linear operator, continuity, neutrosophic normed space

DOI: 10.3233/JIFS-202189

Journal: Journal of Intelligent & Fuzzy Systems, vol. 40, no. 6, pp. 11063-11070, 2021