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Properties of Isometries and Approximate Isometries -
T. Rassias (1999)
Properties of Isometric MappingsJournal of Mathematical Analysis and Applications, 235
- Publisher
- Springer Journals
- Copyright
- Copyright © 2009 by Springer
- Subject
- Mathematics; Mathematics, general; Theoretical, Mathematical and Computational Physics
- ISSN
- 1678-7544
- eISSN
- 1678-7714
- DOI
- 10.1007/s00574-009-0003-2
- Publisher site
- See Article on Publisher Site
Abstract
Let E n be an n-dimensional Euclidean space with n ≥ 2. In this paper, we generalize a classical theorem of Beckman and Quarles by proving that if a mapping, from an open convex subset Co of E n into E n , preserves a distance ρ, then the restriction of f to an open convex subset C ∞ of C 0 is an isometry.
Journal
Bulletin of the Brazilian Mathematical Society, New Series – Springer Journals
Published: Mar 29, 2009