Random Stability of an Additive-Quadratic-Quartic Functional Equation

Using the fixed point method, we prove the generalized Hyers-Ulam stability of the following additive-quadratic-quartic functional equation f(x + 2y) + f (x - 2y) = 2f (x + y) + 2f (-x - y) + 2f (x - y) + 2f(y - x) - 4f(-x) - 2f(x) + f (2y) + f(-2y) - 4f(y) - 4f(-y) in complete random normed spaces.