The norm of continuous linear operator between two fuzzy quasi-normed spaces | Zendy

Han Wang | Zendy; Jianrong Wu | Zendy

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The norm of continuous linear operator between two fuzzy quasi-normed spaces

Author(s) -

Han Wang,

Jianrong Wu

Publication year - 2022

Publication title -

aims mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.329

H-Index - 15

ISSN - 2473-6988

DOI - 10.3934/math.2022655

Subject(s) - mathematics , operator norm , continuous linear operator , linear operators , norm (philosophy) , equivalence (formal languages) , operator (biology) , normed vector space , pure mathematics , operator theory , linear map , fuzzy logic , regular polygon , discrete mathematics , cone (formal languages) , mathematical analysis , algorithm , computer science , biochemistry , chemistry , geometry , repressor , artificial intelligence , political science , transcription factor , law , bounded function , gene

In this paper, firstly, we introduce the concepts of continuity and boundedness of linear operators between two fuzzy quasi-normed spaces with general continuous t -norms, prove the equivalence of them, and point out that the set of all continuous linear operators forms a convex cone. Secondly, we establish the family of star quasi-seminorms on the cone of continuous linear operators, and construct a fuzzy quasi-norm of a continuous linear operator.

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