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A generalized Mazur-Ulam theorem for fuzzy normed spaces

Abstract and Applied Analysis (2014) 2014
DOI: 10.1155/2014/624920
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Abstract

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. © 2014 J. J. Font et al.

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Font, J. J., Galindo, J., Macario, S., & Sanchis, M. (2014). A generalized Mazur-Ulam theorem for fuzzy normed spaces. Abstract and Applied Analysis, 2014. https://doi.org/10.1155/2014/624920

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