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
- SPRINGER INTERNATIONAL PUBLISHING AG
- 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
- Indexed
- SCIE
SCOPUS
- Journal Title
- JOURNAL OF INEQUALITIES AND APPLICATIONS
- Start Page
- 1
- End Page
- 17
- URI
- https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/166546
- DOI
- 10.1186/1029-242X-2012-14
- ISSN
- 1025-5834
- 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.
- Files in This Item
-
Go to Link
- Appears in
Collections - 서울 자연과학대학 > 서울 수학과 > 1. Journal Articles
Items in ScholarWorks are protected by copyright, with all rights reserved, unless otherwise indicated.