A Topological Banach Fixed Point Theorem for Compact Hausdorff Spaces
Canadian mathematical bulletin, Tome 37 (1994) no. 4, pp. 552-555
Voir la notice de l'article provenant de la source Cambridge
We propose an analogue of the Banach contraction principle for connected compact Hausdorff spaces. We define a J-contraction of a connected compact Hausdorff space. We show that every contraction of a compact metric space is a J-contraction and that any J-contraction of a compact metrizable space is a contraction for some admissible metric. We show that every J-contraction has a unique fixed point and that the orbit of each point converges to this fixed point.
Steprans, Juris; Watson, Stephen; Just, Winfried. A Topological Banach Fixed Point Theorem for Compact Hausdorff Spaces. Canadian mathematical bulletin, Tome 37 (1994) no. 4, pp. 552-555. doi: 10.4153/CMB-1994-081-0
@article{10_4153_CMB_1994_081_0,
author = {Steprans, Juris and Watson, Stephen and Just, Winfried},
title = {A {Topological} {Banach} {Fixed} {Point} {Theorem} for {Compact} {Hausdorff} {Spaces}},
journal = {Canadian mathematical bulletin},
pages = {552--555},
year = {1994},
volume = {37},
number = {4},
doi = {10.4153/CMB-1994-081-0},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1994-081-0/}
}
TY - JOUR AU - Steprans, Juris AU - Watson, Stephen AU - Just, Winfried TI - A Topological Banach Fixed Point Theorem for Compact Hausdorff Spaces JO - Canadian mathematical bulletin PY - 1994 SP - 552 EP - 555 VL - 37 IS - 4 UR - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1994-081-0/ DO - 10.4153/CMB-1994-081-0 ID - 10_4153_CMB_1994_081_0 ER -
%0 Journal Article %A Steprans, Juris %A Watson, Stephen %A Just, Winfried %T A Topological Banach Fixed Point Theorem for Compact Hausdorff Spaces %J Canadian mathematical bulletin %D 1994 %P 552-555 %V 37 %N 4 %U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1994-081-0/ %R 10.4153/CMB-1994-081-0 %F 10_4153_CMB_1994_081_0
Cité par Sources :