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

Park, Choonkil; ALACA, CİHANGİR

doi:10.1186/1029-242x-2012-14

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

Park C., ALACA C.

Journal of Inequalities and Applications, vol.2012, 2012 (SCI-Expanded, Scopus)

Publication Type: Article / Article
Volume: 2012
Publication Date: 2012
Doi Number: 10.1186/1029-242x-2012-14
Journal Name: Journal of Inequalities and Applications
Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
Keywords: Mazur-Ulam theorem, alpha-n-norm, 2-fuzzy n-normed linear spaces, n-isometry, n-Lipschitz mapping
Open Archive Collection: AVESIS Open Access Collection
Manisa Celal Bayar University Affiliated: Yes

Abstract

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 nnormed 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. © 2012 Park and Alaca.