Approximate Solutions of an Additive-Quadratic-Quartic (AQQ) Functional Equation

Abstract

In this paper, the authors prove some stability and hyperstability results for an (AQQ): additive-quadratic-quartic functional equation of the form

$$\displaystyle \begin{aligned} \begin{array}{rcl} &\displaystyle &\displaystyle f(x+y+z)+ f(x+y-z)+ f(x-y+z)+f(x-y-z) \\ &\displaystyle &\displaystyle \quad =2[f(x+y)+ f(x-y)+f(y+z)+f(y-z)+ f(x+z)+ f(x-z)] \\ &\displaystyle &\displaystyle \qquad -4f(x) - 4f(y) -2[f(z) + f(-z)] \end{array} \end{aligned} $$

by using fixed point theory.