Generalisations of the Contraction Mapping Theorem : A study on the Generalised Banach Contraction Conjecture
Language: English
Published by LAP LAMBERT Academic Publishing, 2011
- Softcover
- New
Seller: AHA-BUCH GmbH, Einbeck, GermanyAHA-BUCH GmbH
AbeBooks seller since August 14, 2006
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nach der Bestellung gedruckt Neuware - Printed after ordering - Various (putative) generalisations of the Contraction Mapping Theorem in metric space theory in the literature are considered. In particular, generalisations due to Kannan and Suzuki are studied, as is a result of Merryfield, Rothschild and Stein with interesting links to Ramsey theory. The main subsequent business is a question of Stein about when there is a finite family of maps of the metric space, at least one of which contracts any particular pair of points: does some composition of members of the family have to have a unique fixed point The answer is shown to be 'yes' in the special case of two commuting continuous maps of the metric space, but to be 'no' in general, by the counterexample of Austin based on combinatorics on words. Thus in complete generality the Generalised Banach Contraction Conjecture is proven false. Relevant background on metric spaces is also developed.
Seller Inventory # 9783843384797
- Title
- Generalisations of the Contraction Mapping Theorem : A study on the Generalised Banach Contraction Conjecture
- Author
- Christopher Melsa
- Publisher
- LAP LAMBERT Academic Publishing
- Publication year
- 2011
- Condition
- Neu
- Binding
- Taschenbuch
- Language
- English
- ISBN 10
- 3843384797
- ISBN 13
- 9783843384797
- Item weight
- 197 grams
- Dimensions
- 220x150x8 mm
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