The Brouwer Fixed Point Theorem for Some Set Mappings

Volume 61 / 2013

Dariusz Miklaszewski Bulletin Polish Acad. Sci. Math. 61 (2013), 133-140 MSC: Primary 55M20. DOI: 10.4064/ba61-2-6


For some classes $X \subset 2^{\mathbb {B}_n}$ of closed subsets of the disc $\mathbb {B}_n \subset \mathbb {R}^n$ we prove that every Hausdorff-continuous mapping $f : X \rightarrow X$ has a fixed point $A \in X$ in the sense that the intersection $A \cap f(A)$ is nonempty.


  • Dariusz MiklaszewskiFaculty of Mathematics and Computer Science
    Nicolaus Copernicus University
    Chopina 12/18
    87-100 Toruń, Poland

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