Some remarks about K-continuity of K-superquadratic multifunctions

Let X = (X, +) be an arbitrary topological group. The set-valued function F : X → n(Y ) is called K-superquadratic iff F(x + y) + F(x − y) ⊂ 2F(x) + 2F(y) + K, for all x, y ∈ X, where Y denotes a topological vector space and K is a cone. In this paper the K-continuity problem of multifunctions of this kind will be considered with respect to K-boundedness. The case where Y = R^N will be considered separately.