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ON DISTANCE-PRESERVING MAPPINGS
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 Title & Authors
ON DISTANCE-PRESERVING MAPPINGS
Jung, Soon-Mo; M.Rassias, Themistocles;
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 Abstract
We generalize a theorem of W. Benz by proving the following result: Let be a half space of a real Hilbert space with dimension 3 and let Y be a real normed space which is strictly convex. If a distance > 0 is contractive and another distance N (N 2) is extensive by a mapping f : \longrightarrow Y, then the restriction f│ /2// is an isometry, where /2/ is also a half space which is a proper subset of . Applying the above result, we also generalize a classical theorem of Beckman and Quarles.
 Keywords
Aleksandrov problem;isometry;distance-preserving mapping;
 Language
English
 Cited by
1.
The Aleksandrov–Benz–Rassias problem on linear n-normed spaces, Monatshefte für Mathematik, 2016, 180, 2, 305  crossref(new windwow)
2.
The stability of some points arising from continuous, differential and integral expressions, Monatshefte für Mathematik, 2016, 180, 1, 101  crossref(new windwow)
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