Hyers–Ulam stability of additive set-valued functional equations

In this paper, we define the following additive set-valued functional equations equation(1)f(αx+βy)=rf(x)+sf(y),f(αx+βy)=rf(x)+sf(y),equation(2)f(x+y+z)=2f(x+y2)+f(z) for some real numbers α>0,β>0,r,s∈Rα>0,β>0,r,s∈R with α+β=r+s≠1α+β=r+s≠1, and prove the Hyers–Ulam stability of the above additive set-valued functional equations.