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

被引：0
作者：
Choonkil Park
Cihangir Alaca
机构：
[1] Hanyang University,Department of Mathematics, Research Institute for Natural Sciences
[2] Celal Bayar University,Department of Mathematics, Faculty of Science and Arts
来源：
Journal of Inequalities and Applications | / 2012卷
关键词：
Mazur-Ulam theorem; -; -norm; 2-fuzzy ; -normed linear spaces; -isometry; -Lipschitz mapping.;
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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.
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