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.
"Functional Equations Related to Inner Product Spaces." Abstr. Appl. Anal. 2009 1 - 11, 2009. https://doi.org/10.1155/2009/907121