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(2x) + m (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.