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Zbl 0874.47027
Chen, Yu-Qing
On a fixed point problem of Reich.
(English)
[J] Proc. Am. Math. Soc. 124, No.10, 3085-3088 (1996). ISSN 0002-9939; ISSN 1088-6826/e

Let $X$ be a complete metric space, $CB(X)$ the hyperspace of all closed bounded $M\subseteq X$ with the Hausdorff metric, and $F:X\to CB(X)$ a certain local contraction. If $F$ is compact-valued, then {\it S. Reich} [Boll. Unione Mat. Ital., IV. Ser. 5, 26-42 (1972; Zbl 0249.54026)] has shown that $F$ has a fixed point. Here, the author proves the same for $F$ just closed-valued.
[J.Appell (Würzburg)]
MSC 2000:
*47H06 Accretive operators, etc. (nonlinear)
47H10 Fixed point theorems for nonlinear operators on topol.linear spaces
54H25 Fixed-point theorems in topological spaces

Keywords: hyperspace; Hausdorff metric; local contraction; compact-valued; fixed point; closed-valued

Citations: Zbl 0249.54026

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