No CrossRef data available.
Article contents
Uniform Contractification
Published online by Cambridge University Press: 20 November 2018
Abstract
Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.
Let (X, τ) be a metrizable space and {fn: n = 1,2,…} be a commuting family of continuous mappings on X with a common fixed point ξ ∈ X such that (I) for each k = l, 2, …
and (II) 
Then for each c ∈ (0,1), there exists a metric d on X inducing the topology τ such that 
, for all x, y∈X and n = l, 2, …. The above result is also generalized to Tychonoff spaces.
Keywords
- Type
- Research Article
- Information
- Copyright
- Copyright © Canadian Mathematical Society 1978
References
1.
Chew, K. P. and Tan, K. K., Remetrization and family of commuting contractive type mappings, to appear in the Proceedings of the Seminar on fixed point theory and applications, Dalhousie University, 1975.Google Scholar
2.
Goldman, A. J. and Meyers, P. R., Simultaneous contractification, J. Res. NBS, 73B (Math, and Math. Phys.) No. 4, 301-305.Google Scholar
3.
Janos, L., Contraction property of the operator of integration,
Can. Math. Bull.
18 (1975), 367-369.Google Scholar
4.
Jones, L., A converse of Banach's contraction theorem,
Proc. Amer. Math. Soc.
18 (1967), 287-289.Google Scholar
You have
Access