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Contractive multifunctions, fixed point inclusions and iterated multifunction systems

Davide La Torre (), Herb Kunze and Ed Vrscay
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Herb Kunze: University of Guelph, Ontario, Canada
Ed Vrscay: University of Waterloo, Ontario, Canada

No unimi-1025, UNIMI - Research Papers in Economics, Business, and Statistics from Universitá degli Studi di Milano

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.

Keywords: Contractive multifunctions; integral inclusions (search for similar items in EconPapers)
Date: 2006-05-01
Note: oai:cdlib1:unimi-1025
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