| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 6416245 | Linear Algebra and its Applications | 2015 | 8 Pages |
Abstract
Let E be a two-dimensional real normed space. In this paper we show that if the unit circle of E does not contain any line segment such that the distance between its endpoints is greater than 1, then every transformation Ï:EâE which preserves the unit distance is automatically an affine isometry. In particular, this condition is satisfied when the norm is strictly convex.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
György Pál Gehér,