Wszystkie pola: fixed-point property - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: The fixed-point property for deformations of tree-like continua
Autorzy:: Hagopian, Charles
Powiązania:: https://bibliotekanauki.pl/articles/1205393.pdf
Data publikacji:: 1998
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:: fixed point
arc-component
deformation
tree-like continuum
Borsuk ray
dog-chases-rabbit argument
Opis:: Let f be a map of a tree-like continuum M that sends each arc-component of M into itself. We prove that f has a fixed point. Hence every tree-like continuum has the fixed-point property for deformations (maps that are homotopic to the identity). This result answers a question of Bellamy. Our proof resembles an old argument of Brouwer involving uncountably many tangent curves. The curves used by Brouwer were originally defined by Peano. In place of these curves, we use rays that were originally defined by Borsuk.
Źródło:: Fundamenta Mathematicae; 1998, 155, 2; 161-176
0016-2736
Pojawia się w:: Fundamenta Mathematicae
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 2.

Tytuł:: A new convexity property that implies a fixed point property for $L_{1}$
Autorzy:: Lennard, Chris
Powiązania:: https://bibliotekanauki.pl/articles/1293465.pdf
Data publikacji:: 1991
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:: uniform Kadec-Klee property
convergence in measure compact sets
convex sets
normal structure
Lebesgue function spaces
fixed point
nonexpansive mapping
Chebyshev centre
Opis:: In this paper we prove a new convexity property for L₁ that resembles uniform convexity. We then develop a general theory that leads from the convexity property through normal structure to a fixed point property, via a theorem of Kirk. Applying this theory to L₁, we get the following type of normal structure: any convex subset of L₁ of positive diameter that is compact for the topology of convergence locally in measure, must have a radius that is smaller than its diameter. Indeed, a stronger result holds. The Chebyshev centre of any norm bounded, convergence locally in measure compact subset of L₁ must be norm compact. Immediately from normal structure, we get a new proof of a fixed point theorem for L₁ due to Lami Dozo and Turpin.
Źródło:: Studia Mathematica; 1991, 100, 2; 95-108
0039-3223
Pojawia się w:: Studia Mathematica
Dostawca treści:: Biblioteka Nauki

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