Fuzzy Bounded Linear Operators on Fuzzy Anti-Normed Spaces

Jaafer Hmood Eidi^1,*, Aamena Al-Qabani², Fadhel S. Fadhel³, Jehad R. Kider⁴

¹Mustansiriyah University, College of Education, Mathematics Department, Baghdad, Iraq

²Department of Mathematics and Computer Applications, College of Sciences, Al-Nahrain University, Jadriya, Baghdad, Iraq

³Department of Mathematics and Computer Applications, College of Sciences, Al-Nahrain University, Jadriya, Baghdad, Iraq

⁴Department of Applied Sciences, University of Technology, Baghdad, Iraq

Emails: drjaffarmath@uomustansiriyah.edu.iq; aamena.raimmohammed@nahrainuniv.edu.iq; fadhel.subhi@nahrainuniv.edu.iq; jehad.r.kider@uotechnology.edu.iq

Abstract

The primary goal of this paper is to study and introduce fuzzy anti-normed linear spaces, as well as, some additional properties concerning these spaces. From this point of view, some theoretical results are obtained; for example, it was proved that the space of all linear and fuzzy bounded operators over fuzzy anti-normed linear spaces is fuzzy complete. Moreover, some additional theoretical results are stated and proved.

Keywords: Fuzzy bounded operator; Fuzzy anti-normed linear space; Fuzzy anti-norm for bounded operator; Fuzzy anti-metric spaces