K-subquadratic set-valued functions

Let $X=(X,+)$ be an arbitrary topological group. The aim of the paper is to prove a regularity theorem for K-subquadratic set-valued functions, that is, solutions of the inclusion $$2F(s)+2F(t)\subset F(s+t)+F(s-t)+K,s,t\in X,$$ with values in a topological vector space and where $K$ is a cone in this space.