Table of Contents
ISRN Mathematical Analysis
Volume 2013, Article ID 814067, 7 pages
http://dx.doi.org/10.1155/2013/814067
Research Article

On the Mazur-Ulam Theorem in Non-Archimedean Fuzzy -Normed Spaces

School of Mathematics, Beijing Institute of Technology, Beijing 100081, China

Received 11 June 2013; Accepted 4 August 2013

Academic Editors: M. Tang and C. Zhu

Copyright © 2013 Tian Zhou Xu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The motivation of this paper is to present a new notion of non-Archimedean fuzzy -normed space over a field with valuation. We obtain a Mazur-Ulam theorem for fuzzy -isometry mappings in the strictly convex non-Archimedean fuzzy -normed spaces. We also prove that the interior preserving mapping carries the barycenter of a triangle to the barycenter point of the corresponding triangle. And then, using this result, we get a Mazur-Ulam theorem for the interior preserving fuzzy -isometry mappings in non-Archimedean fuzzy -normed spaces over a linear ordered non-Archimedean field.