An introduction to 2-fuzzy n -normed linear spaces and a new perspective to the Mazur-Ulam problem

Journal of inequalities and applications

Choonkil Park¹ 

关键词: Mazur-Ulam theorem;    α-n-norm;    2-fuzzy n-normed linear spaces;    n-isometry;    n-Lipschitz mapping.;   

DOI  :  10.1186/1029-242X-2012-14

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

The 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 ℑ(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.

【 授权许可】

CC BY