International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 66, Pages 3577-3586
Mathematics Section, College of Science and Technology, Hong-Ik University, Chochiwon 339-701, Korea
Received 6 April 2004
Copyright © 2004 Soon-Mo Jung and Byungbae Kim. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We prove that if a one-to-one mapping preserves the unit circles, then is a linear isometry up to translation.