Iteration regularized semigroups of set-valued functions

In this paper, a set-valued iteration regularized semigroup, i.e. a family {F-t}(t >= 0) of set-valued functions for which Fs+t circle C = F-s circle F-t, F-0 = C, s, t >= 0, will be considered, where C is a set-valued function on a closed convex cone in a Banach space. Under some appropriate conditions the generator of a set-valued regularized concave semigroup is introduced and some of its properties are investigated. Also differentiability of the iteration family {C circle F-t}(t >= 0) is discussed.