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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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/151472 |
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| _version_ | 1832556465763647488 |
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| author | Carmen Alegre Salvador Romaguera |
| author_facet | Carmen Alegre Salvador Romaguera |
| author_sort | Carmen Alegre |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-522d89fab00f409cbfd2fdcbd6d91a71 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-522d89fab00f409cbfd2fdcbd6d91a712025-02-03T05:45:15ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/151472151472The Hahn-Banach Extension Theorem for Fuzzy Normed Spaces RevisitedCarmen Alegre0Salvador Romaguera1Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, Camí de Vera, s/n, 46022 Valencia, SpainInstituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, Camí de Vera, s/n, 46022 Valencia, SpainThis 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.http://dx.doi.org/10.1155/2014/151472 |
| spellingShingle | Carmen Alegre Salvador Romaguera The Hahn-Banach Extension Theorem for Fuzzy Normed Spaces Revisited Abstract and Applied Analysis |
| title | The Hahn-Banach Extension Theorem for Fuzzy Normed Spaces Revisited |
| title_full | The Hahn-Banach Extension Theorem for Fuzzy Normed Spaces Revisited |
| title_fullStr | The Hahn-Banach Extension Theorem for Fuzzy Normed Spaces Revisited |
| title_full_unstemmed | The Hahn-Banach Extension Theorem for Fuzzy Normed Spaces Revisited |
| title_short | The Hahn-Banach Extension Theorem for Fuzzy Normed Spaces Revisited |
| title_sort | hahn banach extension theorem for fuzzy normed spaces revisited |
| url | http://dx.doi.org/10.1155/2014/151472 |
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