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An introduction to 2-fuzzy n-normed linear spaces and a new perspective to the Mazur-Ulam problem
- Authors
- Park, Choonkil; Alaca, Cihangir
- Issue Date
- Jan-2012
- Publisher
- Gordon and Breach Science Publishers
- Keywords
- Mazur-Ulam theorem; alpha-n-norm; 2-fuzzy n-normed linear spaces; n-isometry; n-Lipschitz mapping
- Citation
- Journal of Inequalities and Applications, pp 1 - 17
- Pages
- 17
- Indexed
- SCIE
SCOPUS
- Journal Title
- Journal of Inequalities and Applications
- Start Page
- 1
- End Page
- 17
- ISSN
- 1025-5834
1029-242X
- 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 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.
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