Generalized Ulam - Hyers stability of on (AQQ): Additive-quadratic-Quartic functional equation

Abstract

In this paper, the authors obtain the general solution and generalized Ulam - Hyers stability of an (AQQ): additive - quadratic - quartic functional equation of the form
$$
\begin{aligned}
f(x+y+z) & +f(x+y-z)+f(x-y+z)+f(x-y-z) \\
=2[f(x+y) & +f(x-y)+f(y+z)+f(y-z)+f(x+z)+f(x-z)] \\
& -4 f(x)-4 f(y)-2[f(z)+f(-z)]
\end{aligned}
$$
by using the classical Hyers' direct method. Counter examples for non stability are discussed also.