Stability of an additive-quadratic-quartic functional equation

[摘要] In this paper, we investigate the stability of an additive-quadratic-quartic functional equation f(x+2y)+f(x− 2y)− 2f(x+y)− 2f(− x− y)− 2f(x− y)− 2f(y− x)+4f(− x)+2f(x)− f(2y)− f(− 2y)+4f(y)+4f(− y)=0$$\begin{align*}f(x+2y)& +f(x-2y)-2f(x+y)-2f(-x- y)-2f(x-y)-2f(y-x)\nonumber \\ &+4f(-x)+ 2f(x)-f(2y)-f(-2y)+4f(y)+4f(-y)=0 \end{align*}$$ by the direct method in the sense of Găvruta.

[学科分类] 外科医学

[关键词] Hyers-Ulam stability;hyperstability;quadratic functional equation;fixed point theorem