The Hahn-Banach extension theorem for fuzzy normed spaces revisited
type: Item
instance of: scholarly article
title: The Hahn-Banach extension theorem for fuzzy normed spaces revisited
zbMATH Open document ID: 1472.46079
DOI: 10.1155/2014/151472
author: Salvador Romaguera
author: Carmen Alegre
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: This paper deals with fuzzy normed spaces in the sense of \textit{S.-C. Cheng} and \textit{J. N. Mordeson} [Bull. Calcutta Math. Soc. 86, No. 5, 429--436 (1994; Zbl 0829.47063)]. We characterize fuzzy norms in terms of ascending and separating families of seminorms and prove an extension theorem for continuous linear functionals on a fuzzy normed space. Our result generalizes the classical Hahn-Banach extension theorem for normed spaces.
Mathematics Subject Classification ID: 46S40
Mathematics Subject Classification ID: 46A22
zbMATH DE Number: 7021816
zbMATH Keywords: Hahn-Banach extension theorem
zbMATH Keywords: fuzzy normed spaces
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/151472
OpenAlex ID: W2074259866
Wikidata QID: Q59035528
cites work: Fuzzy bounded linear operators
cites work: Fuzzy topological vector spaces. II
cites work: Finite dimensional fuzzy normed linear space
cites work: On fuzzy metric spaces
cites work: Q4846621
cites work: Q4081991
cites work: Q4458997
cites work: Statistical metric spaces
cites work: Characterizations of metrizable topological vector spaces and their asymmetric generalizations in terms of fuzzy (quasi-)norms
cites work: Q3891520
cites work: Q5386174
description: scientific article; zbMATH DE number 7021816