A Generalized Mazur-Ulam Theorem for Fuzzy Normed Spaces

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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Main Authors: J. J. Font, J. Galindo, S. Macario, M. Sanchis
Format: Article
Language:English
Published: Hindawi Limited 2014-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2014/624920
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spelling doaj-482375464c9c4e5db9cde6d753e3e6d22020-11-24T21:43:30ZengHindawi LimitedAbstract 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
collection DOAJ
language English
format Article
sources DOAJ
author J. J. Font
J. Galindo
S. Macario
M. Sanchis
spellingShingle J. J. Font
J. Galindo
S. Macario
M. Sanchis
A Generalized Mazur-Ulam Theorem for Fuzzy Normed Spaces
Abstract and Applied Analysis
author_facet J. J. Font
J. Galindo
S. Macario
M. Sanchis
author_sort J. J. Font
title A Generalized Mazur-Ulam Theorem for Fuzzy Normed Spaces
title_short 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_sort generalized mazur-ulam theorem for fuzzy normed spaces
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2014-01-01
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.
url http://dx.doi.org/10.1155/2014/624920
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