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Let (X, d) be a nonempty metric space, and let (2 X , H d) be the hyperspace of all nonempty compact subsets of X with the Hausdorff metric. Let F : X → 2 X be an ε-contractive map. A general condition is given that guarantees the existence of a periodic point of F (the theorem extends a result of Edelstein to multi-valued maps). The condition holds when X(More)
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