Article contents
A Topological Banach Fixed Point Theorem for Compact Hausdorff Spaces
Published online by Cambridge University Press: 20 November 2018
Abstract
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.
- Type
- Research Article
- Information
- Copyright
- Copyright © Canadian Mathematical Society 1994
References
- 2
- Cited by