The Aleksandrov problem and the Mazur-Ulam theorem on linear $n$-normed spaces
Bull. Korean Math. Soc. 2013 Vol. 50, No. 5, 1631-1637
https://doi.org/10.4134/BKMS.2013.50.5.1631
Published online September 1, 2013
Ma Yumei
Dalian Nationality University
Abstract : 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
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