We show that some multifunctions F : K ! n(Y), satisfying functional inclusions of the form x; F(1(x)); : : : ; F(n(x)) F(x)G(x); admit near-selections f : K ! Y, fulfilling the functional equation x; f (1(x)); : : : ; f (n(x)) = f (x); where functions G : K ! n(Y), : K Yn ! Y and 1; : : : ; n 2 KK are given, n is a fixed positive integer, K is a nonempty set, (Y; ) is a group and n(Y) denotes the family of all nonempty subsets of Y. Our results have been motivated by the notion of Ulam stability and some earlier outcomes. The main tool in the proofs is a very recent fixed point theorem for nonlinear operators, acting on some spaces of multifunctions.