不动点理论和应用(经典英文数学教材系列)(FIXED POINT THEORY AND APPLICATIONS)
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品牌: 拉维加瓦尔
基本信息·出版社：世界图书出版公司
·页码：170 页
·出版日期：2009年
·ISBN：7506292823
·条形码：9787506292825
·包装版本：第1版
·装帧：平装
·开本：24
·正文语种：英语
·丛书名：经典英文数学教材系列
·外文书名：FIXED POINT THEORY AND APPLICATIONS
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内容简介《不动点理论和应用》是“经典英文数学教材系列”之一，全书共分12个章节，主要对不动点理论和应用知识作了介绍，具体内容包括“Contractions”、“Continuation Principles for Condensing Maps”、“Multivalued Maps with Continuous Selections”、“Multivalued Maps with Closed Graph”等。该书可供各大专院校作为教材使用，也可供从事相关工作的人员作为参考用书使用。
编辑推荐《不动点理论和应用》是由世界图书出版公司出版的。
目录
Preface
1 Contractions
2 Nonexpansive Maps
3 Continuation Methods for Contractive and Nonexpansive Mappings
4 The Theorems of Brouwer, Schauder and M5nch
5 Nonlinear Alternatives of Leray-Schauder Type
6 Continuation Principles for Condensing Maps
7 Fixed Point Theorems in Conical Shells
8 Fixed Point Theory in Hausdorff Locally Convex Linear Topological Spaces
9 Contractive and Nonexpansive Multivalued Maps
10 Multivalued Maps with Continuous Selections
11 Multivalued Maps with Closed Graph
12 Degree Theory
Bibliography
Index
……[看更多目录]
序言Perhaps the most well known result in the theory of fixed points is Banach’S contraction mapping principle.It is therefore fitting that we commence this book with a discussion of contractions and a proof of this result.In addition in Chapter 1.a local version and a generalisation of Banach’S contraction theorem are presented.Wle choose the problem of existence and uniqueness of solutions of certain first order initial value problems to demonstrate the results detailed in the chapter.
It iS inevitable that any discussion on contractive maps will lead naturally to another on nonexpansive maps，which is why we choose this as the topic of Chapter 2.Schauder’S theorem for nonexpansive maps is presented but the main theorem discussed is a result proved inde- pendently in 1965 by Browder.G5hde and Kirk which shows that each nonexpansive map F：C+C.where C is a particular set in a Hilbert space，has at least one fixed point.As a natural lead in to the next chap- ter，we close Chapter 2 with a nonlinear alternative of Leray-Schauder type for nonexpansive maps.
Chapter 3 is concerned with continuation methods for contractive and nonexpansive maps.We show initially that the property of having a fixed point is invariant by homotopy for COntractions.Using this result a non- linear alternative of Leray-Schauder type is presented for contractive maps and subsequently generalised for nonexpansive maps.An applica- tion of the nonlinear alternative for contractions is demonstrated with a second order homogeneous Dirichlet problem.
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