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

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

Author(s) -

Tian Zhou Xu

Publication year - 2013

Publication title -

isrn mathematical analysis

Language(s) - English

Resource type - Journals

eISSN - 2090-4665

pISSN - 2090-4657

DOI - 10.1155/2013/814067

Subject(s) - mathematics , isometry (riemannian geometry) , normed vector space , fuzzy logic , field (mathematics) , valuation (finance) , pure mathematics , discrete mathematics , regular polygon , computer science , geometry , finance , artificial intelligence , economics

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.

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