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Iterated Function Systems on Multifunctions

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  • Davide La Torre

    (University of Milan)

  • Edward Vrscay

    (University of Waterloo)

  • Franklin Mendivil

    (Acadia University)

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    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.

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    Bibliographic Info

    Paper provided by Universit√° degli Studi di Milano in its series UNIMI - Research Papers in Economics, Business, and Statistics with number unimi-1024.

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    Date of creation: 01 Mar 2006
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    Handle: RePEc:bep:unimip:unimi-1024

    Note: oai:cdlib1:unimi-1024
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    Keywords: Iterated Function Systems; Multifunctions; Set Valued Analysis;

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