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Contractive multifunctions, fixed point inclusions and iterated multifunction systems |
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| Authors: | HE Kunze ER Vrscay |
| Institution: | a Department of Mathematics and Statistics, University of Guelph, Guelph, Ontario, Canada N16 2W1 b Department of Economics, Business and Statistics, University of Milan, Italy c Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1 |
| Abstract: | We study the properties of multifunction operators that are contractive in the Covitz-Nadler sense. In this situation, such operators T possess fixed points satisfying the relation x∈Tx. We introduce an iterative method involving projections that guarantees convergence from any starting point x0∈X to a point x∈XT, the set of all fixed points of a multifunction operator T. We also prove a continuity result for fixed point sets XT 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 Iterated multifunction systems Iterated function systems Optimization |
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