Stability of a Functional Equation Deriving from Cubic and Quartic Functions

Abstract

We obtain the general solution and the generalized Ulam-Hyers stability of the cubic and quartic functional equation $4\left(f\left(3x+y\right)+f\left(3x-y\right)\right)=-12\left(f\left(x+y\right)+f\left(x-y\right)\right)+12\left(f\left(2x+y\right)+f\left(2x-y\right)\right)-8f\left(y\right)-192f\left(x\right)+f\left(2y\right)+30f\left(2x\right)$.