A Generalized Mazur‐Ulam Theorem for Fuzzy Normed Spaces

J. J. Font, J. Galindo, S. Macario and M. Sanchis

Abstract and Applied Analysis, 2014, vol. 2014, issue 1

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.

Date: 2014
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https://doi.org/10.1155/2014/624920

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:624920

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