Generalized Hyers-Ulam Stability of a Mixed Type Functional Equation

Abstract

We investigate the stability of a functional equation $f\left(x+y+z\right)$ $+$ $f\left(x-y+z\right)$ $+$ $f\left(x+y-z\right)+f\left(-x+y+z\right)=3f\left(x\right)+f\left(-x\right)+3f\left(y\right)+f\left(-y\right)+3f\left(z\right)+f\left(-z\right)$ by applying the direct method in the sense of Hyers and Ulam.