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Fixed points for contractive multifunctions


Author: R. E. Smithson
Journal: Proc. Amer. Math. Soc. 27 (1971), 192-194
MSC: Primary 54.85
DOI: https://doi.org/10.1090/S0002-9939-1971-0267564-4
MathSciNet review: 0267564
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Abstract: Let $ F:X \to X$ be a point closed multifunction on the bounded metric space $ (X,d)$. Let $ \hat d$ denote the Hausdorff metric for the nonempty closed subsets of $ X$. Then $ F$ is contractive iff $ \hat d(F(x),F(y)) < d(x,y)$ for all $ x,y \in X$. We give conditions under which contractive multifunctions have fixed points.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1971-0267564-4
Keywords: Contractive multivalued functions, fixed point theorems, orbits for multifunctions, regular orbits, cluster points of orbits
Article copyright: © Copyright 1971 American Mathematical Society

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