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Generalisations of the Contraction Mapping Theorem

 

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  • Product Description
 

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.

Product Specifications
SKU :COC93536
AuthorChristopher Melsa
LanguageEnglish
BindingPaperback
Number of Pages120
Publishing Year2011-01-18T00:00:00.000
ISBN978-3843384797
Edition1 st
Book TypeMathematics
Country of ManufactureIndia
Product BrandLAP LAMBERT Academic Publishing
Product Packaging InfoBox
In The Box1 Piece
Product First Available On ClickOnCare.com2015-08-14 00:00:00