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Generalisations of the Contraction Mapping Theorem: A study on the Generalised Banach Contraction Conjecture - Christopher Melsa
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Christopher Melsa:
Generalisations of the Contraction Mapping Theorem: A study on the Generalised Banach Contraction Conjecture - Taschenbuch

ISBN: 3843384797

Paperback, [EAN: 9783843384797], LAP LAMBERT Academic Publishing, LAP LAMBERT Academic Publishing, Book, [PU: LAP LAMBERT Academic Publishing], LAP LAMBERT Academic Publishing, 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., 13884, Mathematics, 226699, Applied, 226700, Geometry & Topology, 13942, History, 13944, Infinity, 13955, Mathematical Analysis, 13957, Matrices, 13961, Number Systems, 13965, Popular & Elementary, 226698, Pure Mathematics, 13979, Reference, 13981, Research, 13985, Study & Teaching, 13989, Transformations, 13991, Trigonometry, 75, Science & Math, 1000, Subjects, 283155, Books

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Generalisations of the Contraction Mapping Theorem - Taschenbuch

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[EAN: 9783843384797], Neubuch, [PU: LAP Lambert Academic Publishing], CHRISTOPHER MELSA,MATHEMATICS, Paperback. 120 pages. Dimensions: 9.0in. x 6.0in. x 0.4in.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. This item ships from multiple locations. Your book may arrive from Roseburg,OR, La Vergne,TN.

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2011, ISBN: 9783843384797

ID: 629826206

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. A study on the Generalised Banach Contraction Conjecture Bücher > Fremdsprachige Bücher > Englische Bücher Taschenbuch 19.01.2011 Buch (fremdspr.), LAP Lambert Academic Publishing, .201

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Generalisations of the Contraction Mapping Theorem: A study on the Generalised Banach Contraction Conjecture - Christopher Melsa
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Christopher Melsa:
Generalisations of the Contraction Mapping Theorem: A study on the Generalised Banach Contraction Conjecture - Taschenbuch

ISBN: 3843384797

Taschenbuch, [EAN: 9783843384797], LAP LAMBERT Academic Publishing, LAP LAMBERT Academic Publishing, Book, [PU: LAP LAMBERT Academic Publishing], LAP LAMBERT Academic Publishing, 56214011, Mathematik, 1320308031, Abbildungen, 56248011, Angewandte Mathematik, 1320307031, Forschung, 56263011, Geometrie & Topologie, 56212011, Geschichte, 56227011, Lernen & Lehren, 56217011, Mathematische Analyse, 56272011, Mathematische Physik, 56218011, Matrizen, 56219011, Messung, 56225011, Nachschlagewerke, 56221011, Populär & Elementar, 56230011, Reine Mathematik, 1320309031, Trigonometrie, 56216011, Unendlichkeit, 56220011, Zahlensysteme, 56047011, Wissenschaft, 54071011, Genres, 52044011, Fremdsprachige Bücher

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Generalisations of the Contraction Mapping Theorem - Taschenbuch

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Generalisations of the Contraction Mapping Theorem

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.

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EAN (ISBN-13): 9783843384797
ISBN (ISBN-10): 3843384797
Gebundene Ausgabe
Taschenbuch
Erscheinungsjahr: 2011
Herausgeber: AV Akademikerverlag GmbH & Co. KG.

Buch in der Datenbank seit 30.08.2007 02:46:41
Buch zuletzt gefunden am 25.07.2017 14:44:42
ISBN/EAN: 9783843384797

ISBN - alternative Schreibweisen:
3-8433-8479-7, 978-3-8433-8479-7


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