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title[*]contributor[author]contributor[advisor]keywords[*]date[issued] publisher citationsidentifier[uri]identifier[doi]abstractrelation[journal]relation[volume]relation[no]relation[page]aAn introduction to 2-fuzzy n-normed linear spaces and a new perspective to the Mazur-Ulam problem8bMazur-Ulam theorem;
alpha-n-norm;
2-fuzzy n-normed linear spaces;
n-isometry;
n-Lipschitz mapping;2012-01$SPRINGER INTERNATIONAL PUBLISHING AG<JOURNAL OF INEQUALITIES AND APPLICATIONS, 2012, P.1-17, P.17`https://journalofinequalitiesandapplications.springeropen.com/articles/10.1186/1029-242X-2012-1410.1186/1029-242X-2012-14SThe purpose of this article is to introduce the concept of 2-fuzzy n-normed linear space or fuzzy n-normed linear space of the set of all fuzzy sets of a non-empty set. We define the concepts of n-isometry, n-collinearity n-Lipschitz mapping in this space. Also, we generalize the Mazur-Ulam theorem, that is, when X is a 2-fuzzy n-normed linear space or a"(X) is a fuzzy n-normed linear space, the Mazur-Ulam theorem holds. Moreover, it is shown that each n-isometry in 2-fuzzy n-normed linear spaces is affine. Mathematics Subject Classification (2010): 03E72; 46B20; 51M25; 46B04; 46S40.(JOURNAL OF INEQUALITIES AND APPLICATIONS1-17&HQsj&)KLngKmTvWy@/Qz
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