Communications of the
Korean Mathematical Society CKMS

Let $f: \mathbb R^3 \to \mathbb R $. In this paper we prove the stability of functional inequalities \begin{align} |f(ux+vy, uy-vx,zw)-f(x, y,z)f(u,v,w)|&\le\phi(u, v, w) \,\, {\rm or}\,\,\phi(x, y, z), \nonumber \\ |f(ux-vy, uy-vx,zw)-f(x, y,z)f(u,v,w)|&\le\phi(u, v, w) \,\,{\rm or}\,\,\phi(x, y, z) \nonumber \end{align} for all $x,y,z,u,v,w \in \mathbb R$. Furthermore, we give refined descriptions of bounded functions satisfying the inequalities as in Albert and Baker \cite{AB}.

Keywords: determinant, exponential functional equation, multiplicative function, stability

MSC numbers: 39B82