Fixed Points (Mathematical World) [Paperback]

Yu. A. Shashkin (Author)

Book Description

ISBN-10: 082189000X | ISBN-13: 978-0821890004 | Publication Date: November 1991

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.

Editorial Reviews

Language Notes

Text: English (translation)
Original Language: Russian

Product Details

• Paperback: 86 pages
• Publisher: Amer Mathematical Society (November 1991)
• Language: English
• ISBN-10: 082189000X
• ISBN-13: 978-0821890004
• Product Dimensions: 9.8 x 6.8 x 0.3 inches
• Shipping Weight: 6.4 ounces
• Average Customer Review: 4.0 out of 5 stars  See all reviews (1 customer review)
• Amazon Best Sellers Rank: #2,086,302 in Books (See Top 100 in Books)

Customer Reviews

Most Helpful Customer Reviews

3 of 4 people found the following review helpful:

4.0 out of 5 stars It can be used as a refresher or as a primer, August 30, 2002

By 

Charles Ashbacher (Marion, Iowa United States) - See all my reviews
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This review is from: Fixed Points (Mathematical World) (Paperback)

Many mathematical problems are solved by applying a fixed point theorem, so it is advantageous for all mathematicians to learn a great deal about them. As the title indicates, the purpose of this book is to present the fundamentals of fixed point theorems, and in that capacity, it is well worth reading. The basics of the concept of fixed points are demonstrated in an understandable, yet complete manner. Many diagrams are included as well as over fifty supplemental problems with solutions. Therefore, it can serve as either a supplemental or refresher text in the more detailed points of what is a critical and widely used area of mathematics. I strongly recommend that it be included in all academic mathematics libraries.