The Hahn-Banach Extension Theorem for Fuzzy Normed Spaces Revisited

This paper deals with fuzzy normed spaces in the sense of Cheng and Mordeson. 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-Ban...

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Bibliographic Details
Published inAbstract and Applied Analysis Vol. 2014; no. 2014; pp. 868 - 874
Main Authors Alegre, C., Romaguera, Salvador
Format Journal Article
LanguageEnglish
Published Cairo, Egypt Hindawi Limiteds 01.01.2014
Hindawi Publishing Corporation
John Wiley & Sons, Inc
Hindawi Limited
Wiley
Subjects
Banach spaces
Fuzzy algorithms
Fuzzy logic
Fuzzy systems
Mathematical research
Theorems (Mathematics)
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Summary:This paper deals with fuzzy normed spaces in the sense of Cheng and Mordeson. 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.
ISSN:1085-3375
1687-0409
DOI:10.1155/2014/151472