The Brouwer Fixed Point Theorem for Some Set Mappings
Volume 61 / 2013
Bulletin Polish Acad. Sci. Math. 61 (2013), 133-140
MSC: Primary 55M20.
DOI: 10.4064/ba61-2-6
Abstract
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.
