On the stability of the generalized cubic set-valued functional equation

In this article, we focus on the set-valued dynamics related to the theory of functional equations. We study the n -dimensional cubic set-valued functional equation f ( ∑ j = 1 n − 1 x j + 2 x n ) ⊕ f ( ∑ j = 1 n − 1 x j − 2 x n ) ⊕ ∑ j = 1 n − 1 f ( 2 x j ) = 2 f ( ∑ j = 1 n − 1 x j ) ⊕ 4 ∑ j = 1 n − 1 ( f ( x j + x n ) ⊕ f ( x j − x n ) ) where n ≥ 2 is an integer. We also prove the Hyers–Ulam stability for the set-valued functional equation.