G-Fuzzy Operator Norm

S. Chatterjee and T. Bag ()
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S. Chatterjee: Department of Mathematics, Siksha-Bhavana, Visva-Bharati, Santiniketan, Birbhum, West-Bengal 731235, India
T. Bag: Department of Mathematics, Siksha-Bhavana, Visva-Bharati, Santiniketan, Birbhum, West-Bengal 731235, India

New Mathematics and Natural Computation (NMNC), 2023, vol. 19, issue 02, 325-347

Abstract: In our previous paper, it is shown that topology of G-fuzzy normed linear space is generated by two types of open balls: one is elliptic and the other is circular. In the theoretical aspect of functional analysis, will this type of exception happen or not? To address this problem in this paper, firstly, G-fuzzy bounded linear operators as well as G-fuzzy bounded linear functionals are defined which are the key elements of functional analysis. Then, operator G-fuzzy norms are introduced for both the cases using the idea of quasi-G-norm family. The definition of operator G-fuzzy norm is quite different from the existing operator fuzzy norm. Completeness of operator G-fuzzy norm is investigated. Lastly, Hahn-Banach theorem in G-fuzzy setting is studied using all the above concepts.

Keywords: G-fuzzy norm; fuzzy normed linear space; t-norm; G-fuzzy operator norm (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S1793005723500102

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