Hyers–Ulam stability of additive set-valued functional equations

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