Department of Mathematics, Research Institute for Natural Sciences, Hanyang University, Seoul 133-791, Republic of Korea
Copyright © 2010 Choonkil Park. 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.
Rassias introduced the following equality , , for a fixed integer . Let be real vector spaces. It is shown that, if a mapping satisfies the following functional equation for all with , which is defined by the above equality, then the mapping is realized as the sum of an additive mapping and a quadratic mapping. Using the fixed point method, we prove the generalized Hyers-Ulam stability of the above functional equation in real Banach spaces.