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Contractive multifunctions, fixed point inclusions and iterated multifunction systems
Davide La Torre, University of Milan
Herb Kunze, University of Guelph, Ontario, Canada
Ed Vrscay, University of Waterloo, Ontario, Canada
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ABSTRACT:
We study the properties of multifunction operators that are contractive in the
Covier-Nadler sense. In this situation, such operators $T$ possess fixed
points satisying the relation $x \in Tx$. We introduce an iterative method
involving projections that guarantees convergence from any starting point $x_0
\in X$ to a point $x \in X_T$, the set of all fixed points of a multifunction
operator $T$. We also prove a continuity result for fixed point sets $X_T$ as
well as a ``generalized collage theorem'' for contractive multifunctions.
These results can then be used to solve inverse problems involving contractive
multifunctions. Two applications of contractive multifunctions are introduced:
(i) integral inclusions and (ii) iterated multifunction systems.
SUGGESTED CITATION:
Davide La Torre, Herb Kunze, and Ed Vrscay,
"Contractive multifunctions, fixed point inclusions and iterated multifunction systems"
(May 2006).
UNIMI - Research Papers in Economics, Business, and Statistics.
Statistics and Mathematics.
Working Paper 10.
http://services.bepress.com/unimi/statistics/art10
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