THE ALEKSANDROV PROBLEM AND THE MAZUR-ULAM THEOREM ON LINEAR n-NORMED SPACES

Title & Authors
THE ALEKSANDROV PROBLEM AND THE MAZUR-ULAM THEOREM ON LINEAR n-NORMED SPACES
Yumei, Ma;

Abstract
This paper generalizes the Aleksandrov problem and Mazur Ulam theorem to the case of $\small{n}$-normed spaces. For real $\small{n}$-normed spaces X and Y, we will prove that $\small{f}$ is an affine isometry when the mapping satisfies the weaker assumptions that preserves unit distance, $\small{n}$-colinear and 2-colinear on same-order.
Keywords
n-DOPP;n-isometry;n-Lipschitz;2-collinear;n-collinear;
Language
English
Cited by
1.
The Aleksandrov–Benz–Rassias problem on linear n-normed spaces, Monatshefte für Mathematik, 2016, 180, 2, 305
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