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Iterated function systems on multifunctions and inverse problems

Author

Listed:
  • Davide LA TORRE
  • Franklin MENDIVIL

Abstract

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 set-valued 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

Suggested Citation

  • Davide LA TORRE & Franklin MENDIVIL, 2007. "Iterated function systems on multifunctions and inverse problems," Departmental Working Papers 2007-032, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.
    • Handle: RePEc:mil:wpdepa:2007-032
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