Stability of a Quartic Functional Equation

We obtain the general solution of the generalized quartic functional equation f(x + my) + f(x - my) = 2(7m - 9) (m - 1) f(x) + 2m(2)(m(2) - 1) f(y) - (m - 1)(2){f(x + y) + f(x - y)} for a fixed positive integer m. We prove the Hyers-Ulam stability for this quartic functional equation by the directed method and the fixed point method on real Banach spaces. We also investigate the Hyers- Ulam stability for the mentioned quartic functional equation in non-Archimedean spaces.