Fixed Point Theory [Paperback]

The theory of Fixed Points is one of the most powerful tools of modern mathematics. This book contains a clear, detailed and well-organized presentation of the major results, together with an entertaining set of historical notes and an extensive bibliography describing further developments and applications.

From the reviews: I recommend this excellent volume on fixed point theory to anyone interested in this core subject of nonlinear analysis. --MATHEMATICAL REVIEWS

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 developed in 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.Elementary Fixed Point Theorems * Theorem of Borsuk and Topological Transversality * Homology and Fixed Points * Leray-Schauder Degree and Fixed Point Index * The Lefschetz-Hopf Theory * Selected Topics * Index

Frol“Y