Ulam Stability of a Quartic Functional Equation

Abstract

The oldest quartic functional equation was introduced by J. M. Rassias in (1999), and then was employed by other authors. The functional equation $f(2x+y)+f(2x-y)=4f(x+y)+4f(x-y)+24f\left(x\right)-6f\left(y\right)$ 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.