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http://dx.doi.org/10.4134/BKMS.2013.50.5.1631

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

Yumei, Ma (Department of Mathematics Dalian Nationality University)
Publication Information
Bulletin of the Korean Mathematical Society / v.50, no.5, 2013 , pp. 1631-1637 More about this Journal
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;
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