A Generalized Mazur-Ulam Theorem for Fuzzy Normed Spaces. (2nd June 2014) - Font, J. J.; Galindo, J.; Macario, S.; Sanchis, M.
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.