On approximate additive-quartic and quadratic-cubic functional equations in two variables on Abelian groups (Q708725)

The authors prove the generalized Hyers-Ulam stability for the systems of additive-quartic functional equations \[ \begin{cases} f(x_1+x_2,y)=f(x_1,y)+f(x_2,y),\\ f(x,2y_1+y_2)+f(x,2y_1-y_2)=4f(x,y_1+y_2) +4f(x,y_1-y_2)+24f(x,y_1)-6f(x,y_2). \end{cases} \] and the quadratic-cubic functional equations \[ \begin{cases} f(x,2y_1+y_2)+f(x,2y_1-y_2)=2f(x,y_1+y_2)+2f(x,y_1-y_2)+12f(x,y_1)\\ f(x,y_1+y_2)+f(x,y_1-y_2)=2f(x,y_1)+2f(x,y_2). \end{cases} \] where \(f\) is a mapping with two variables on abelian groups.