The Brouwer Fixed Point Theorem for Some Set Mappings

• Autorzy: Miklaszewski D.

Identyfikatory

DOI

10.4064/ba61-2-6

• Języki publikacji: EN

Abstrakty

EN

For some classes X⊂2^Bn of closed subsets of the disc B_n⊂Rⁿ we prove that every Hausdorff-continuous mapping f:X→X has a fixed point A∈X in the sense that the intersection A∩f(A) is nonempty.

Słowa kluczowe

EN

fixed points

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2013
• Tom: Vol. 61, no 2
• Strony: 133--140
• Opis fizyczny: Bibliogr. 5 poz.

Twórcy

autor

Miklaszewski D.

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

Bibliografia

• [1] K. Borsuk, On some metrization of the hyperspace of compact sets, Fund. Math. 41 (1954), 168–202.
• [2] L. Górniewicz, Topological Fixed Point Theory of Multivalued Mappings, Kluwer, 1999.
• [3] C. Gorzka, Mereology versus Topology and Pointless Geometry, Nicolaus Copernicus Univ. Torun, 2003 (in Polish).
• [4] S.-T. Hu, Homotopy Theory, Academic Press, New York, 1959.
• [5] S. Kakutani, A generalization of Brouwer’s fixed point theorem, Duke Math. J. 8 (1941), 457–459.