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2014 A Generalized Mazur-Ulam Theorem for Fuzzy Normed Spaces
J. J. Font, J. Galindo, S. Macario, M. Sanchis
Abstr. Appl. Anal. 2014: 1-4 (2014). DOI: 10.1155/2014/624920


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:XY be a fuzzy norm-preserving surjection satisfying f(0)=0. Then f is additive.


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J. J. Font. J. Galindo. S. Macario. M. Sanchis. "A Generalized Mazur-Ulam Theorem for Fuzzy Normed Spaces." Abstr. Appl. Anal. 2014 1 - 4, 2014.


Published: 2014
First available in Project Euclid: 2 October 2014

zbMATH: 07022759
MathSciNet: MR3219379
Digital Object Identifier: 10.1155/2014/624920

Rights: Copyright © 2014 Hindawi

Vol.2014 • 2014
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