TY - JOUR
AU - 박춘길
DA - 2012/01
PY - 2012
UR - https://journalofinequalitiesandapplications.springeropen.com/articles/10.1186/1029-242X-2012-14
AB - 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.
PB - SPRINGER INTERNATIONAL PUBLISHING AG
KW - Mazur-Ulam theorem
KW - alpha-n-norm
KW - 2-fuzzy n-normed linear spaces
KW - n-isometry
KW - n-Lipschitz mapping
TI - An introduction to 2-fuzzy n-normed linear spaces and a new perspective to the Mazur-Ulam problem
DO - 10.1186/1029-242X-2012-14
T2 - JOURNAL OF INEQUALITIES AND APPLICATIONS
ER -