A Generalized Mazur-Ulam Theorem for Fuzzy Normed Spaces
We introduce fuzzy norm-preserving maps, which generalize the concept of fuzzy isometry. Based on the ideas from Vogt, 1973, and Väisälä, 2003, we provide the following generalized version of the Mazur-Ulam theorem in the fuzzy context: let X, Y be fuzzy normed spaces and let f:X→Y be a fuzzy norm-p...
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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/10.1155/2014/624920 |
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| author | J. J. Font J. Galindo S. Macario M. Sanchis |
| author_facet | J. J. Font J. Galindo S. Macario M. Sanchis |
| author_sort | J. J. Font |
| collection | DOAJ |
| description | We introduce fuzzy norm-preserving maps, which generalize the concept of fuzzy isometry. Based on the ideas from Vogt, 1973, and Väisälä, 2003, we provide the following generalized version of the Mazur-Ulam theorem in the fuzzy context: let X, Y be fuzzy normed spaces and let f:X→Y be a fuzzy norm-preserving surjection satisfying f(0)=0. Then f is additive. |
| format | Article |
| id | doaj-art-482375464c9c4e5db9cde6d753e3e6d2 |
| institution | OA Journals |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-482375464c9c4e5db9cde6d753e3e6d22025-08-20T02:38:01ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/624920624920A Generalized Mazur-Ulam Theorem for Fuzzy Normed SpacesJ. J. Font0J. Galindo1S. Macario2M. Sanchis3Departament de Matemàtiques, Institut Universitari de Matemàtiques i Aplicacions de Castelló (IMAC), Universitat Jaume I, Campus del Riu Sec. s/n, 12071 Castelló, SpainDepartament de Matemàtiques, Institut Universitari de Matemàtiques i Aplicacions de Castelló (IMAC), Universitat Jaume I, Campus del Riu Sec. s/n, 12071 Castelló, SpainDepartament de Matemàtiques, Institut Universitari de Matemàtiques i Aplicacions de Castelló (IMAC), Universitat Jaume I, Campus del Riu Sec. s/n, 12071 Castelló, SpainDepartament de Matemàtiques, Institut Universitari de Matemàtiques i Aplicacions de Castelló (IMAC), Universitat Jaume I, Campus del Riu Sec. s/n, 12071 Castelló, SpainWe introduce fuzzy norm-preserving maps, which generalize the concept of fuzzy isometry. Based on the ideas from Vogt, 1973, and Väisälä, 2003, we provide the following generalized version of the Mazur-Ulam theorem in the fuzzy context: let X, Y be fuzzy normed spaces and let f:X→Y be a fuzzy norm-preserving surjection satisfying f(0)=0. Then f is additive.http://dx.doi.org/10.1155/2014/624920 |
| spellingShingle | J. J. Font J. Galindo S. Macario M. Sanchis A Generalized Mazur-Ulam Theorem for Fuzzy Normed Spaces Abstract and Applied Analysis |
| title | A Generalized Mazur-Ulam Theorem for Fuzzy Normed Spaces |
| title_full | A Generalized Mazur-Ulam Theorem for Fuzzy Normed Spaces |
| title_fullStr | A Generalized Mazur-Ulam Theorem for Fuzzy Normed Spaces |
| title_full_unstemmed | A Generalized Mazur-Ulam Theorem for Fuzzy Normed Spaces |
| title_short | A Generalized Mazur-Ulam Theorem for Fuzzy Normed Spaces |
| title_sort | generalized mazur ulam theorem for fuzzy normed spaces |
| url | http://dx.doi.org/10.1155/2014/624920 |
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