Ulam Stability of a Quartic Functional Equation

The oldest quartic functional equation was introduced by J. M. Rassias in (1999), and then was employed by other authors. The functional equation f (2x + y) + f (2x - y) = 4f (x + y) + 4f (x - y) + 24f (x)- 6f (y) is called a quartic functional equation, all of its solution is said to be a quartic function. In the current paper, the Hyers-Ulam stability and the superstability for quartic functional equations are established by using the fixed-point alternative theorem.