- Title
- Completeness and the contraction principle
- Creator
- Borwein, J. M.; Huang, W. Z.
- Relation
- Proceedings of the American Mathematical Society Vol. 87, Issue 2, p. 246-250
- Publisher Link
- http://dx.doi.org/10.1090/S0002-9939-1983-0681829-1
- Publisher
- American Mathematical Society (AMS)
- Resource Type
- journal article
- Date
- 1983
- Description
- We prove (something more general than) the result that a convex subset of a Banach space is closed if and only if every contraction of the space leaving the convex set invariant has a fixed point in that subset. This implies that a normed space is complete if and only if every contraction on the space has a fixed point. We also show that these results fail if "convex" is replaced by "Lipschitz-connected" or "starshaped".
- Subject
- contraction mapping; complete metric space; Ekeland's principle
- Identifier
- http://hdl.handle.net/1959.13/940540
- Identifier
- uon:13036
- Identifier
- ISSN:0002-9939
- Rights
- First published in Proceedings of the American Mathematical Society in Vol. 87, No. 2, pp. 246-250, 1983, published by the American Mathematical Society.
- Language
- eng
- Full Text
- Reviewed
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|---|---|---|---|---|---|---|---|
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