On the stability problem for a mixed type of quartic and quadratic functional equation

Let E1E1 and E2E2 be real linear spaces. In this paper, we determine the general solution for a mixed type functional equation of a quartic and a quadratic mapping f:E1→E2f:E1→E2,⊎x2,…,xnn−1f(x1)+2n−1(n−2)∑i=1nf(xi)=2n−2∑1⩽i2n>2. In addition we solve the generalized Hyers–Ulam–Rassias stability problem for the functional equation.