On a bi-quadratic functional equation and its stability Original Research Article

In this paper, we obtain the general solution and the generalized Hyers–Ulam stability of the bi-quadratic functional equation f(x+y,z+w)+f(x+y,z-w)+f(x-y,z+w)+f(x-y,z-w)=4[f(x,z)+f(x,w)+f(y,z)+f(y,w)].