Just define your operator ():
I chose to return a reference to the functor (standard approach), but you can return whatever you like - even void.
template <typename Iterator>
const SomeProcess& operator ()(Iterator pos, Iterator end)
// do something useful...
template <typename Container>
const SomeProcess& operator ()(Container& box)
return (*this)(box.begin(), box.end());
Oh, and if you design a functor to operate on an object within a container, you could use it in functions like std::for_each, etc.