It is proved that if \(C\) is a closed convex cone in a Banach space and \(G:C\to cc(C)\) is a continuous linear set-valued function, then for every \(x\in C\) and \(t\geq 0\) the series \[ B^t(x)= \sum^\infty_{i=0} {t^i\over i!} G^i(x) \] is convergent. Moreover, the set-valued functions \(B^t\) are linear, continuous on \(\text{int C}\) and it holds \((B^t\circ B^s)(x)\subset B^{s+t}(x)\) for all \(s,t\geq 0\) and \(x\in C\).