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Iterated function systems on multifunctions and inverse problems

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  • 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

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Bibliographic Info

Paper provided by Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano in its series Departmental Working Papers with number 2007-32.

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Date of creation: 24 Sep 2007
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Handle: RePEc:mil:wpdepa:2007-32

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Keywords: IFS operators; Set Valued Analysis; Inner Product; Multifunctions; Convex Sets;

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Cited by:
  1. La Torre, Davide & Marsiglio, Simone & Privileggi, Fabio, 2011. "Fractals and Self-Similarity in Economics: the Case of a Stochastic Two-Sector Growth Model," POLIS Working Papers 157, Institute of Public Policy and Public Choice - POLIS.

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