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Research Article | Open Access

Hahn-Banach type theorems and the separation of convex sets for fuzzy quasi-normed spaces

Ruini Li, Jianrong Wu( )
College of Mathematics Science, Suzhou University of Science and Technology, Suzhou, Jiangsu 215009, P. R. China
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Abstract

In this paper, we first study continuous linear functionals on a fuzzy quasi-normed space, obtain a characterization of continuous linear functionals, and point out that the set of all continuous linear functionals forms a convex cone and can be equipped with a weak fuzzy quasi-norm. Next, we prove a theorem of Hahn-Banach type and two separation theorems for convex subsets of fuzzy quasinormed spaces.

Keywords

fuzzy quasi-normed spacecontinuous linear functionalHahn-Banach extension theoremseparation theorem
CLC number: 46S40, 46B10

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AIMS Mathematics
Volume 7 Issue 3,
March 2022
Pages 3290-3302
DOI: 10.3934/math.2022183

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Cite this article:
Li R, Wu J. Hahn-Banach type theorems and the separation of convex sets for fuzzy quasi-normed spaces. AIMS Mathematics, 2022, 7(3): 3290-3302. https://doi.org/10.3934/math.2022183

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Received: 08 October 2021
Accepted: 25 November 2021
Published: 15 March 2021
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)