On Hukuhara’s differentiable iteration semigroups of linear set-valued functions

In this paper, we investigate the uniform convergence of continuous linear set-valued functions on compact sets. We also consider conditions under which the family of continuous linear extensions of a differential iteration semigroup of continuous linear set-valued functions is a differentiable iteration semigroup. In particular, since the cones and normed spaces are not supposed to be complete our main results generalize some recent results on Hukuhara’s derivative of set-valued functions.