Generalisations of the Contraction Mapping Theorem

Language: English

Published by LAP LAMBERT Academic Publishing Jan 2011, 2011

3843384797 / 9783843384797

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This item is printed on demand - Print on Demand Titel. Neuware -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.VDM Verlag, Dudweiler Landstraße 99, 66123 Saarbrücken 120 pp. Englisch. …

Seller Inventory # 9783843384797

Title
Generalisations of the Contraction Mapping Theorem
Author
Christopher Melsa
Publisher
LAP LAMBERT Academic Publishing Jan 2011
Publication year
2011
Condition
Neu
Binding
Taschenbuch
Language
English
ISBN 10
3843384797
ISBN 13
9783843384797
Item weight
197 grams
Dimensions
220x150x8 mm

buchversandmimpf2000

Emtmannsberg, BAYE, Germany

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