Contractive multifunctions, xed point inclusions and iterated multifunction systems

Abstract. We study the properties of multifunction operators that are contractive in the Covitz-Nadler sense. In this situation, such opera-tors T possess xed points satisying the relation x 2 Tx. We introduce an iterative method involving projections that guarantees convergence from any starting point x0 2 X to a point x 2 XT, the set of all xed points of a multifunction operator T. We also prove a continuity result for xed point sets XT as well as a \generalized collage theorem " for contractive multifunctions. These results can then be used to solve in-verse problems involving contractive multifunctions. Two applications of contractive multifunctions are introduced: (i) integral inclusions and (ii) iterated multifunction systems. AMS Subject Classication: 41A, 65D1