Bulletin of the
Korean Mathematical Society BKMS

This paper generalizes the Aleksandrov problem and Mazur Ulam theorem to the case of $n$-normed spaces. For real $n$-normed spaces $X$ and $Y$, we will prove that $f$ is an affine isometry when the mapping satisfies the weaker assumptions that preserves unit distance, $n$-colinear and 2-colinear on same-order.

Keywords: $n$-DOPP, $n$-isometry, $n$-Lipschitz, $2$-collinear, $n$-collinear

MSC numbers: 46B04, 46B20, 51K05