doi:10.1155/2008/628178 Research Article On the Stability of Quadratic Functional Equations

Let X,Y be vector spaces and k a fixed positive integer. It is shown that a mapping fkx y fkx − y 2k2fx 2fy for all x, y ∈ X if and only if the mapping f: X → Y satisfies fx y fx − y 2fx 2fy for all x, y ∈ X. Furthermore, the Hyers-Ulam-Rassias stability of the above functional equation in Banach spaces is proven. Copyright q 2008 Jung Rye Lee 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. 1