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 nn-dimensional cubic set-valued functional equation f(∑j=1n−1xj+2xn)⊕f(∑j=1n−1xj−2xn)⊕∑j=1n−1f(2xj)=2f(∑j=1n−1xj)⊕4∑j=1n−1(f(xj+xn)⊕f(xj−xn)) where n≥2n≥2 is an integer. We also prove the Hyers–Ulam stability for the set-valued functional equation.