Granas / Dugundji Fixed Point Theory

Erscheinungsjahr 2013
ISBN: 978-0-387-21593-8
Verlag: Springer US
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 690 Seiten, eBook

Reihe: Springer Monographs in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Granas, Andrzej

Dugundji, James

Inhaltsverzeichnis

§0. Introduction.- I. Elementary Fixed Point Theorems.- II. Theorem of Borsuk and Topological Transversality.- III. Homology and Fixed Points.- IV. Leray-Schauder Degree and Fixed Point Index.- V. The Lefschetz-Hopf Theory.- VI. Selected Topics.- Appendix: Preliminaries.- A. Generalities.- B. Topological Spaces.- C. Linear Topological Spaces.- D. Algebraic Preliminaries.- E. Categories and Functors.- I. General Reference Texts.- II. Monographs, Lecture Notes, and Surveys.- III. Articles.- IV. Additional References.- List of Standard Symbols.- Index of Names.- Index of Terms.

Über Autor(innen)

Andrzej Granas studied in Warsaw and then Moscow, where he earned his doctorate in 1958 under Lazar Lusternik. Since 1958 he has held various research and teaching posts in Poland, Canada, and elsewhere. During the Spring of 1970 he occupied a special chair at the Collège de France. In the early nineties, Dr. Granas founded the journal Topological Methods of Nonlinear Analysis, and since 1992, he has served on the Editorial Board of the Zentralblatt. He is an honorary member of the Gdansk Scientific Society.