Solution and Stability of a General Mixed Type Cubic and Quartic Functional Equation

Abstract EN

We consider the following mixed type cubic and quartic functional equation λ[f(x+λy)+f(x-λy)] = λ3[f(x+y)+f(x-y)]-2λ3(λ+1)f(y)-2λ(λ2-1)f(x)+2(λ+1)f(λy), where λ is a fixed integer.

We establish the general solution of the functional equation when the integer λ≠0, ±1, and then, by using the fixed point alternative, we investigate the generalized Hyers-Ulam-Rassias stability for this functional equation when the integer λ≥2.