Fixed points for contractive multifunctions
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- by R. E. Smithson PDF
- Proc. Amer. Math. Soc. 27 (1971), 192-194 Request permission
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.References
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Additional Information
- © Copyright 1971 American Mathematical Society
- 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