# Fixed Points

## Shashkin, Yu A.

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The theory of fixed points finds its roots in the work of Poincare, Brouwer, and Sperner and makes extensive use of such topological notions as continuity, compactness, homotopy, and the degree of a mapping. Fixed point theorems have numerous applications in mathematics; most of the theorems ensuring the existence of solutions for differential, integral, operator, or other equations can be reduced to fixed point theorems. In addition, these theorems are used in such areas as mathematical economics and game theory. This book presents a readable exposition of fixed point theory. The author focuses on the problem of whether a closed interval, square, disk, or sphere has the fixed point property. Another aim of the book is to show how fixed point theory uses combinatorial ideas related to decomposition (triangulation) of figures into distinct parts called faces (simplexes), which adjoin each other in a regular fashion. All necessary background concepts - such as continuity, compactness, degree of a map, and so on - are explained, making the book accessible even to students at the high school level. In addition, the book contains exercises and descriptions of applications. Readers will appreciate this book for its lucid presentation of this fundamental mathematical topic.

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Contenuti:

Continuous mapping of a closed interval and a square; First combinatorial lemma; Second combinatorial lemma, or walks through the rooms in a house; Sperner's lemma; Continuous mapping, homeomorphisms, and the fixed point property; Compactness; Proof of Brouwer's Theorem for a closed interval, the intermediate value theorem, and applications; Proof of Brouwer's Theorem for a square; The iteration method; Retraction; Continuous mappings of a circle, homotopy, and degree of a mapping; Second definition of the degree of mapping; Continuous mappings of a sphere; Lemma in equality of degrees.

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## 1.Fixed Points (Mathematical World)

Editore: Amer Mathematical Society (1991)
ISBN 10: 082189000X ISBN 13: 9780821890004
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Descrizione libro Amer Mathematical Society, 1991. Paperback. Condizione libro: New. Codice libro della libreria SONG082189000X

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## 2.Fixed Points (Paperback)

Editore: American Mathematical Society, United States (1991)
ISBN 10: 082189000X ISBN 13: 9780821890004
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Descrizione libro American Mathematical Society, United States, 1991. Paperback. Condizione libro: New. 249 x 173 mm. Language: English . Brand New Book. The theory of fixed points finds its roots in the work of Poincare, Brouwer, and Sperner and makes extensive use of such topological notions as continuity, compactness, homotopy, and the degree of a mapping. Fixed point theorems have numerous applications in mathematics; most of the theorems ensuring the existence of solutions for differential, integral, operator, or other equations can be reduced to fixed point theorems. In addition, these theorems are used in such areas as mathematical economics and game theory. This book presents a readable exposition of fixed point theory. The author focuses on the problem of whether a closed interval, square, disk, or sphere has the fixed point property.Another aim of the book is to show how fixed point theory uses combinatorial ideas related to decomposition (triangulation) of figures into distinct parts called faces (simplexes), which adjoin each other in a regular fashion. All necessary background concepts - such as continuity, compactness, degree of a map, and so on - are explained, making the book accessible even to students at the high school level. In addition, the book contains exercises and descriptions of applications. Readers will appreciate this book for its lucid presentation of this fundamental mathematical topic. Codice libro della libreria AAN9780821890004

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## 3.Fixed Points (Paperback)

Editore: American Mathematical Society, United States (1991)
ISBN 10: 082189000X ISBN 13: 9780821890004
Nuovi Paperback Quantità: 1
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Descrizione libro American Mathematical Society, United States, 1991. Paperback. Condizione libro: New. 249 x 173 mm. Language: English . Brand New Book. The theory of fixed points finds its roots in the work of Poincare, Brouwer, and Sperner and makes extensive use of such topological notions as continuity, compactness, homotopy, and the degree of a mapping. Fixed point theorems have numerous applications in mathematics; most of the theorems ensuring the existence of solutions for differential, integral, operator, or other equations can be reduced to fixed point theorems. In addition, these theorems are used in such areas as mathematical economics and game theory. This book presents a readable exposition of fixed point theory. The author focuses on the problem of whether a closed interval, square, disk, or sphere has the fixed point property.Another aim of the book is to show how fixed point theory uses combinatorial ideas related to decomposition (triangulation) of figures into distinct parts called faces (simplexes), which adjoin each other in a regular fashion. All necessary background concepts - such as continuity, compactness, degree of a map, and so on - are explained, making the book accessible even to students at the high school level. In addition, the book contains exercises and descriptions of applications. Readers will appreciate this book for its lucid presentation of this fundamental mathematical topic. Codice libro della libreria AAN9780821890004

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## 4.Fixed Points

ISBN 10: 082189000X ISBN 13: 9780821890004
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Descrizione libro Condizione libro: New. Depending on your location, this item may ship from the US or UK. Codice libro della libreria 97808218900040000000

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## 5.Fixed Points

Editore: American Mathematical Society
ISBN 10: 082189000X ISBN 13: 9780821890004
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Descrizione libro American Mathematical Society. Paperback. Condizione libro: new. BRAND NEW, Fixed Points, Yu A. Shashkin, The theory of fixed points finds its roots in the work of Poincare, Brouwer, and Sperner and makes extensive use of such topological notions as continuity, compactness, homotopy, and the degree of a mapping. Fixed point theorems have numerous applications in mathematics; most of the theorems ensuring the existence of solutions for differential, integral, operator, or other equations can be reduced to fixed point theorems. In addition, these theorems are used in such areas as mathematical economics and game theory. This book presents a readable exposition of fixed point theory. The author focuses on the problem of whether a closed interval, square, disk, or sphere has the fixed point property.Another aim of the book is to show how fixed point theory uses combinatorial ideas related to decomposition (triangulation) of figures into distinct parts called faces (simplexes), which adjoin each other in a regular fashion. All necessary background concepts - such as continuity, compactness, degree of a map, and so on - are explained, making the book accessible even to students at the high school level. In addition, the book contains exercises and descriptions of applications. Readers will appreciate this book for its lucid presentation of this fundamental mathematical topic. Codice libro della libreria B9780821890004

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## 6.Fixed Points (Mathematical World)

Editore: Ameican Mathematical Society (1991)
ISBN 10: 082189000X ISBN 13: 9780821890004
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Descrizione libro Ameican Mathematical Society, 1991. Paperback. Condizione libro: New. Brand new. We distribute directly for the publisher. The theory of fixed points finds its roots in the work of Poincaré, Brouwer, and Sperner and makes extensive use of such topological notions as continuity, compactness, homotopy, and the degree of a mapping. Fixed point theorems have numerous applications in mathematics; most of the theorems ensuring the existence of solutions for differential, integral, operator, or other equations can be reduced to fixed point theorems. In addition, these theorems are used in such areas as mathematical economics and game theory.This book presents a readable exposition of fixed point theory. The author focuses on the problem of whether a closed interval, square, disk, or sphere has the fixed point property. Another aim of the book is to show how fixed point theory uses combinatorial ideas related to decomposition (triangulation) of figures into distinct parts called faces (simplexes), which adjoin each other in a regular fashion. All necessary background concepts--such as continuity, compactness, degree of a map, and so on--are explained, making the book accessible even to students at the high school level. In addition, the book contains exercises and descriptions of applications. Readers will appreciate this book for its lucid presentation of this fundamental mathematical topic. Codice libro della libreria 1005130077

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## 7.Fixed Points

Editore: American Mathematical Society (1991)
ISBN 10: 082189000X ISBN 13: 9780821890004
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Descrizione libro American Mathematical Society, 1991. PAP. Condizione libro: New. New Book. Shipped from UK in 4 to 14 days. Established seller since 2000. Codice libro della libreria CE-9780821890004

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## 8.Fixed Points

Editore: Amer Mathematical Society (1991)
ISBN 10: 082189000X ISBN 13: 9780821890004
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Descrizione libro Amer Mathematical Society, 1991. Paperback. Condizione libro: Brand New. 86 pages. 10.00x7.00x0.25 inches. In Stock. Codice libro della libreria __082189000X

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## 9.Fixed Points (Mathematical World)

Editore: Amer Mathematical Society (1991)
ISBN 10: 082189000X ISBN 13: 9780821890004
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Descrizione libro Amer Mathematical Society, 1991. Paperback. Condizione libro: New. book. Codice libro della libreria 082189000X

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## 10.Fixed Points (Mathematical World)

Editore: Amer Mathematical Society (1991)
ISBN 10: 082189000X ISBN 13: 9780821890004
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Descrizione libro Amer Mathematical Society, 1991. Paperback. Condizione libro: New. First Printing. Codice libro della libreria DADAX082189000X

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