Ulam Stability of a Quartic Functional Equation

Abstract EN

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.