Copyright © 2009 Choonkil Park et al. 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.
Let be real vector spaces. It is shown that an odd mapping
satisfies for all if and only if the odd mapping is Cauchy additive. Furthermore, we prove the generalized Hyers-Ulam stability of the above functional equation
in real Banach spaces.