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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

Suggested Citation

  • Davide LA TORRE & Franklin MENDIVIL, 2007. "Iterated function systems on multifunctions and inverse problems," Departmental Working Papers 2007-32, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.
    • Handle: RePEc:mil:wpdepa:2007-32
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    File URL: http://wp.demm.unimi.it/files/wp/2007/DEMM-2007_032wp.pdf
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    References listed on IDEAS

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    1. Davide La Torre & Herb Kunze & Ed Vrscay, 2006. "Contractive multifunctions, fixed point inclusions and iterated multifunction systems," UNIMI - Research Papers in Economics, Business, and Statistics unimi-1025, Universitá degli Studi di Milano.
    2. Davide La Torre & Edward Vrscay & Franklin Mendivil, 2006. "Iterated Function Systems on Multifunctions," UNIMI - Research Papers in Economics, Business, and Statistics unimi-1024, Universitá degli Studi di Milano.
    3. Davide La Torre & Franklin Mendivil, 2006. "Markov operators on multimeasures," UNIMI - Research Papers in Economics, Business, and Statistics unimi-1031, Universitá degli Studi di Milano.
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    Cited by:

    1. Herb E. KUNZE & Davide LA TORRE & Edward R. VRSCAY, 2008. "From iterated function systems to iterated multifunction systems," Departmental Working Papers 2008-39, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.
    2. La Torre, Davide & Marsiglio, Simone & Mendivil, Franklin & Privileggi, Fabio, 2015. "Self-similar measures in multi-sector endogenous growth models," Chaos, Solitons & Fractals, Elsevier, vol. 79(C), pages 40-56.
    3. D. La Torre & F. Mendivil, 2022. "Stochastic efficiency and inefficiency in portfolio optimization with incomplete information: a set-valued probability approach," Annals of Operations Research, Springer, vol. 311(2), pages 1085-1098, April.
    4. 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.
    5. D. La Torre & F. Mendivil, 2018. "Portfolio optimization under partial uncertainty and incomplete information: a probability multimeasure-based approach," Annals of Operations Research, Springer, vol. 267(1), pages 267-279, August.

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    4. La Torre, Davide & Marsiglio, Simone & Mendivil, Franklin & Privileggi, Fabio, 2015. "Self-similar measures in multi-sector endogenous growth models," Chaos, Solitons & Fractals, Elsevier, vol. 79(C), pages 40-56.

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