Iterated function systems on multifunctions and inverse problems
AbstractIn 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 InfoPaper 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.
Date of creation: 24 Sep 2007
Date of revision:
IFS operators; Set Valued Analysis; Inner Product; Multifunctions; Convex Sets;
This paper has been announced in the following NEP Reports:
- NEP-ALL-2009-06-17 (All new papers)
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