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Iterated Function Systems on Multifunctions

Author

Listed:
  • Davide La Torre

    (University of Milan)

  • Edward Vrscay

    (University of Waterloo)

  • Franklin Mendivil

    (Acadia University)

Abstract

We introduce a method of iterated function systems (IFS) over the space of set-valued mappings (multifunctions). This is done by first considering a couple of useful metrics over the space of multifunctions F(X,Y). Some appropriate IFS-type fractal transform operators T:F(X,Y)->F(X,Y) are then defined which combine spatially-contracted and range-modified copies of a multifunction u to produce a new multifunction v = Tu. Under suitable conditions, the fractal transform T is contractive, implying the existence of a fixed-point set-valued mapping u. Some simple examples are then presented. We then consider the inverse problem of approximation of set-valued mappings by fixed points of fractal transform operators T and present some preliminary results.

Suggested Citation

  • 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.
    • Handle: RePEc:bep:unimip:unimi-1024
    Note: oai:cdlib1:unimi-1024
    as

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    Citations

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    Cited by:

    1. 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.
    2. 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.
    3. Davide LA TORRE & Edward R. VRSCAY & Mehran EBRAHIMI & Michael F. BARNSLEY, 2008. "Measure-valued images, associated fractal transforms and the affine self-similarity of images," Departmental Working Papers 2008-45, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.

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