On an n-dimensional mixed type additive and quadratic functional equation

In this paper, we investigate the generalized Hyers-Ulam stability of the functional equation∑k2,…,kn=01fx1+∑i=2n(-1)kixi-2n-1f(x1)-2n-2∑i=2nf(xi)+f(-xi)=0for integer values of n such that n⩾2, where f is a function from a normed space X to a Banach space Y. The solutions of the equation are called additive-quadratic mappings.