In this paper, we first consider the problem of defining IFS operators on the space K_C of non-empty compact and convex subsets of R^d. After defining a complete metric on K_C, we construct an IFS operator and show some properties. A notable feature is the definition of a type of weak inner product on K_C. We then define a family of complete metrics on the space of all measurable set-valued functions (with values in K_C), 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

Iterated function systems on multifunctions and inverse problems / D. La Torre, F. Mendivil. - In: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. - ISSN 0022-247X. - 340:2(2008 Apr 15), pp. 1469-1479.

Iterated function systems on multifunctions and inverse problems

D. La Torre
Primo
;
2008

Abstract

In this paper, we first consider the problem of defining IFS operators on the space K_C of non-empty compact and convex subsets of R^d. After defining a complete metric on K_C, we construct an IFS operator and show some properties. A notable feature is the definition of a type of weak inner product on K_C. We then define a family of complete metrics on the space of all measurable set-valued functions (with values in K_C), 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
Convex sets; IFS operators; Inner product; Multifunctions; Set valued analysis
Settore SECS-S/06 - Metodi mat. dell'economia e Scienze Attuariali e Finanziarie
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/52669
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