A Generalized Mazur-Ulam Theorem for Fuzzy Normed Spaces. (2nd June 2014)

• Record Type: Journal Article
• Authors: Font, J. J.; Galindo, J.; Macario, S.; Sanchis, M.
• Other Names: Romaguera Salvador Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2014(2014)
• Publication Date: 2014-06-02
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2014/624920
• Languages: English
• ISSNs: 1085-3375

Abstract

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.