Iterated function systems on multifunctions and inverse problems

In this paper, we first consider the problem of defining IFS operators on the space K_C of non-empty compact and convex subsets of R^d. After defining a complete metric on K_C, we construct an IFS operator and show some properties. A notable feature is the definition of a type of weak inner product on K_C. We then define a family of complete metrics on the space of all measurable set-valued functions (with values in K_C), and extend the weak inner product to this space. Following this, we construct IFS operators on these spaces. We close with a brief discussion of the inverse problem of approximating an arbitrary multifunction by the attractor of an IFS