Approximation of the mixed additive and cubic functional equation in paranormed spaces

In this paper, we prove some theorems about the HyersUlam stability of the functional equation f(2x + y) + f(2x - y) = 2f(x + y) + 2f(x - y) + 2[f(2x) - 2f(x)] in paranormed spaces. From these theorems, as corollaries, we obtain the stability of the above functional equation with weaker conditions controlled by product of powers of norms and mixedtype productsum of powers of norms.