Fixed Point Theory
Fixed Point Theory
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DOI：
10.1007/978-0-387-21593-8
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发表时间：
2003-06
期刊：
影响因子：
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通讯作者：
A. Granas;J. Dugundji
中科院分区：
文献类型：
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作者：
A. Granas;J. Dugundji
本专著的目的是对不动点理论中处于拓扑和非线性泛函分析边界线上的经典主题进行统一说明，强调与勒雷·绍德理论相关的发展。主要使用几何方法，我们的研究围绕着为许多现代数学领域的结果奠定基础的理论的一般原理。正文是自成一体的读者与拓扑和功能分析适度的知识；必要的背景资料收集在附录中，或根据需要发展。只有最后一章预设了对代数拓扑更高级部分的一些熟悉。“杂项的结果和例子”，在以往的形式给出，形成了书的一个组成部分，并描述了进一步的应用和扩展的理论。这些额外的结果大多可以通过书中提出的方法来建立，正文中没有任何证据依赖于其中的任何一个；要求更高的问题用星号标记。段落末尾的“注释和评注”包含对文献的参考，并提供有关文本结果的进一步信息。
The aim of this monograph is to give a unified account of the classical topics in fixed point theory that lie on the border-line of topology and non linear functional analysis, emphasizing developments related to the Leray Schauder theory. Using for the most part geometric methods, our study cen ters around formulating those general principles of the theory that provide the foundation for many of the modern results in diverse areas of mathe matics. The main text is self-contained for readers with a modest knowledge of topology and functional analysis; the necessary background material is collected in an appendix, or developed as needed. Only the last chapter pre supposes some familiarity with more advanced parts of algebraic topology. The" Miscellaneous Results and Examples", given in the form of exer cises, form an integral part of the book and describe further applications and extensions of the theory. Most of these additional results can be established by the methods developedin the book, and no proof in the main text relies on any of them; more demanding problems are marked by an asterisk. The" Notes and Comments" at the end of paragraphs contain references to the literature and give some further information about the results in the text.