Christopher Melsa (6 results)

Taschenbuch. Condition: Neu. Generalisations of the Contraction Mapping Theorem | A study on the Generalised Banach Contraction Conjecture | Christopher Melsa | Taschenbuch | 120 S. | Englisch | 2011 | LAP LAMBERT Academic Publishing | EAN 9783843384797 | Verantwortliche Person für die EU: preigu GmbH & Co. KG, Lengericher Landstr. 19, 49078 Osnabrück, mail[at]preigu[dot]de | Anbieter: preigu.…

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Taschenbuch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - 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. 120 pp. Englisch.…

Condition: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Autor/Autorin: Melsa ChristopherObtained First Class Honours Degree in Mathematics at Essex University. A particular interest was discovered in the field of Metric Spaces and my passion for research gave way to two years studying towards a Master.…

Taschenbuch. Condition: Neu. 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.…

Taschenbuch. Condition: Neu. 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.…