Abstract and Applied Analysis
Volume 2009 (2009), Article ID 907121, 11 pages
doi:10.1155/2009/907121
Functional equations related to inner product spaces
Choonkil Park1
, Won-Gil Park2
and Abbas Najati3
1Department of Mathematics, Hanyang University, Seoul 133-791, South Korea
2National Institute for Mathematical Sciences, Daejeon 305-340, South Korea
3Department of Mathematics, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil 51664, Iran
Abstract
Let V,W be real vector spaces. It is shown that an odd mapping f:V→W satisfies ∑i−12nf(xi−1/2n∑j=12nxj)=∑i=12nf(xi)−2nf(1/2n∑i=12nxi) for all x1,…,x2n∈V if and only if the odd mapping f:V→W is Cauchy additive. Furthermore, we prove the generalized Hyers-Ulam stability of the above functional equation in real Banach spaces.