On the Ulam stability of an n-dimensional quadratic functional equation

In the present paper, we construct a new n-dimensional quadratic functional equation with constant coefficients n∑i,j=1f(xi+xj)=2n∑1≤i j≤nf(xi−xj)+4f(n∑i=1xi) And then, we study the Ulam stability of the preceding equation in a real normed space and a non- Archimedean space, respectively.