Abstract and Applied Analysis
Volume 2008 (2008), Article ID 628178, 8 pages
doi:10.1155/2008/628178
On the stability of quadratic functional equations
Jung Rye Lee1
, Jong Su An2
and Choonkil Park3
1Department of Mathematics, Daejin University, Kyeonggi 487-711, South Korea
2Department of Mathematics Education, Pusan National University, Pusan 609-735, South Korea
3Department of Mathematics, Hanyang University, Seoul 133-791, South Korea
Abstract
Let X,Y be vector spaces and k a fixed positive integer. It is shown that a mapping f(kx+y)+f(kx-y)=2k2f(x)+2f(y) for all x,y∈X if and only if the mapping f:X→Y satisfies f(x+y)+f(x-y)=2f(x)+2f(y) for all x,y∈X. Furthermore, the Hyers-Ulam-Rassias stability of the above functional equation in Banach spaces is proven.