Periodic Points of Multi-valued Ε-contractive Maps
نویسندگان
چکیده
Let (X, d) be a nonempty metric space, and let (2X , Hd) be the hyperspace of all nonempty compact subsets of X with the Hausdorff metric. Let F :X → 2X 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 is compact; hence, F has a periodic point when X is compact. It is shown that F has a fixed point (a point p ∈ F (p)) if X is a continuum. Applications to single-valued ε-expansive maps are given.
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