Using the Mazur–Orlicz theorem and some results about the Fréchet functional equation, we consider functional equations related to generalized monomials of degree n. From these considerations, we give some results on existence of single-valuedness and selections for convex-valued maps satisfying functional inclusions. Also, the Diaz–Margolis fixed point alternative is applied to solve the stability problem for set-valued generalized monomials of degree n. Finally, several particular cases are discussed and some applications are given.
