|
|
libcats.org
Fixed PointsYu. A. ShashkinThe 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.
Популярные книги за неделю:
Проектирование и строительство. Дом, квартира, садАвтор: Петер Нойферт, Автор: Людвиг Нефф
Размер книги: 20.83 Mb
Система упражнений по развитию способностей человека (Практическое пособие)Автор: Петров Аркадий НаумовичКатегория: Путь к себе
Размер книги: 818 Kb
Сотворение мира (3-х томник)Автор: Петров Аркадий НаумовичКатегория: Путь к себе
Размер книги: 817 Kb
Радиолюбительские схемы на ИС типа 555Автор: Трейстер Р.Категория: Электротехника и связь
Размер книги: 13.64 Mb
Genki 1: An Integrated Course in Elementary Japanese 1Автор: Eri Banno, Автор: Yutaka Ohno, Автор: Yoko Sakane, Автор: Chikako Shinagawa, Автор:
Размер книги: 172.22 Mb
Только что пользователи скачали эти книги:
Optimal trading strategiesАвтор: Robert Kissell, Автор: Morton GlantzКатегория: Mathematics, Optimization and control
Размер книги: 3.53 Mb
Handbook of pharmaceutical excipients (Rowe, Handbook of Pharmaceutical Excipients)Автор: Pharmaceutical Press
Размер книги: 25.00 Mb
Было ли начало мираАвтор: проф. Р. В. КуницкийКатегория: КНИГИ НАУЧНО-ПОПУЛЯРНОЕ
Размер книги: 1.48 Mb
|
|
|