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3 Bulletin of the Polish Academy of Sciences. Mathematics

3 Miklaszewski D.

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The Brouwer Fixed Point Theorem for Some Set Mappings

Miklaszewski D.

Bulletin of the Polish Academy of Sciences. Mathematics

2013

Vol. 61, no 2

133--140

For some classes X⊂2Bn of closed subsets of the disc Bn⊂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.

Fixed Points of Maps of Sets of Polyhedra into the Disc

Miklaszewski D.

Bulletin of the Polish Academy of Sciences. Mathematics

2013

Vol. 61, no 3-4

263--275

We prove that Platonic and some Archimedean polyhedra have the fixed point property in a non-classical sense.

An application of the Stiefel-Whitney classes to the proof of a fixed point theorem for set-valued mappings

Miklaszewski D.

Bulletin of the Polish Academy of Sciences. Mathematics

2005

Vol. 53, no 2

181-186

We prove a fixed point theorem for Borsuk continuous mappings with spherical values, which extends a previous result. We apply some nonstandard properties of the Stiefel-Whitney classes.