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On distance-preserving mappings
- Authors
- Jung, SM; Rassias, TM
- Issue Date
- Jul-2004
- Publisher
- KOREAN MATHEMATICAL SOC
- Keywords
- Aleksandrov problem; isometry; distance-preserving mapping
- Citation
- JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY, v.41, no.4, pp.667 - 680
- Journal Title
- JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY
- Volume
- 41
- Number
- 4
- Start Page
- 667
- End Page
- 680
- ISSN
- 0304-9914
- Abstract
- We generalize a theorem of W. Benz by proving the following result: Let H(theta) be a half space of a real Hilbert space with dimension greater than or equal to 3 and let Y be a real normed space which is strictly convex. If a distance p > 0 is contractive and another distance Nrho (N greater than or equal to 2) is extensive by a mapping f : H(theta) --> Y, then the restriction f\H(theta+rho/2) is an isometry, where H(theta+rho/2) is also a half space which is a proper subset of H(theta). Applying the above result, we also generalize a. classical theorem of Beckman and Quarles.
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