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MAPPINGS OF CONSERVATIVE DISTANCES IN
$p$-NORMED SPACES (
$0<p\leq 1$)
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 95 / Issue 2 / April 2017
- Published online by Cambridge University Press:
- 02 November 2016, pp. 291-298
- Print publication:
- April 2017
-
- Article
-
- You have access
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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.
