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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.
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- Research Article
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- © 2016 Australian Mathematical Publishing Association Inc.