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

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 - Christopher Melsa
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Generalisations of the Contraction Mapping Theorem - Livres de poche

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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 - Livres de poche

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

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
Version reliée
Livre de poche
Date de parution: 2011
Editeur: AV Akademikerverlag GmbH & Co. KG.

Livre dans la base de données depuis 30.08.2007 02:46:41
Livre trouvé récemment le 25.07.2017 14:44:42
ISBN/EAN: 9783843384797

ISBN - Autres types d'écriture:
3-8433-8479-7, 978-3-8433-8479-7


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