Iterated function systems on multifunctions and inverse problems

In this paper, we first consider the problem of defining IFS operators on the space Kc of non-empty compact and convex subsets of Rd . After defining a complete metric on Kc, we construct an IFS operator and show some properties. A notable feature is the definition of a type of weak inner product on Kc. We then define a family of complete metrics on the space of all measurable setvalued functions (with values in Kc), 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. © 2007 Elsevier Inc. All rights reserved.