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MAPPINGS OF CONSERVATIVE DISTANCES IN
$p$-NORMED SPACES (
$0<p\leq 1$)
Published online by Cambridge University Press: 02 November 2016
Abstract
We show that any mapping between two real $p$-normed spaces, which preserves the unit distance and the midpoint of segments with distance
$2^{p}$, is an isometry. Making use of it, we provide an alternative proof of some known results on the Aleksandrov question in normed spaces and also generalise these known results to
$p$-normed spaces.
MSC classification
- Type
- Research Article
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- Copyright
- © 2016 Australian Mathematical Publishing Association Inc.