Iterated Function Systems on Multifunctions
Davide La Torre, University of Milan
Edward Vrscay, University of Waterloo
Franklin Mendivil, Acadia University
Download the Paper (PDF format) - March 1, 2006
Tell a colleague about it.
Printing Tips: Select 'print as image' in the Acrobat print dialog if you have trouble printing.
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.
SUBJECT AREA:
41A, 65D15
SUGGESTED CITATION:
Davide La Torre, Edward Vrscay, and Franklin Mendivil,
"Iterated Function Systems on Multifunctions"
(March 2006).
UNIMI - Research Papers in Economics, Business, and Statistics.
Statistics and Mathematics.
Working Paper 8.
http://services.bepress.com/unimi/statistics/art8
Paper presented by Pieralda Ferrari.
| 
