A Mazur-Ulam theorem for Mappings of conservative distance in non-Archimedean $n$-normed spaces

TL;DR

This paper extends the Mazur-Ulam theorem to non-Archimedean n-normed spaces, exploring properties of n-isometries and their behavior in these specialized mathematical structures.

Contribution

It introduces a Mazur-Ulam type theorem for non-Archimedean n-normed spaces and analyzes properties of n-isometries in this context.

Findings

Proved the Mazur-Ulam theorem in non-Archimedean n-normed spaces

Established properties of n-isometries in these spaces

Extended classical results to non-Archimedean setting

Abstract

In this article, we study the notions of $n$-isometries in non-Archimedean $n$-normed spaces over linear ordered non-Archimedean fields, and prove the Mazur-Ulam theorem in the spaces. Furthermore, we obtain some properties for $n$-isometries in non-Archimedean $n$-normed spaces.