This book provides a clear exposition of the flourishing field of fixed point theory. Starting from the basics of Banach's contraction theorem, most of the main results and techniques are developed: fixed point results are established for several classes of maps and the three main approaches to establishing continuation principles are presented. The theory is applied to many areas of interest in analysis. Topological considerations play a crucial role, including a final chapter on the relationship with degree theory. Researchers and graduate students in applicable analysis will find this to be a useful survey of the fundamental principles of the subject. The very extensive bibliography and close to 100 exercises mean that it can be used both as a text and as a comprehensive reference work, currently the only one of its type.
Rezensionen / Stimmen
'... can be considered as a handbook containing an introduction from the metric and topological fixed-point theory.' Lech Gorniewicz, Zentralblatt fur Mathematik
Reihe
Sprache
Verlagsort
Zielgruppe
Illustrationen
Worked examples or Exercises
Maße
Höhe: 235 mm
Breite: 157 mm
Dicke: 15 mm
Gewicht
ISBN-13
978-0-521-80250-5 (9780521802505)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Klassifikation
Autor*in
National University of Singapore
Dublin City University
National University of Ireland, Galway
Preface; 1. Contradictions; 2. Non-expansive maps; 3. Continuation methods for contractive and non-expansive mapping; 4. The theorems of Brouwer, Svhauder and Monch; 5. Non-linear 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 non-expansive multivalued maps; 10. Multivalued maps with continuous selections; 11. Multivalued maps with closed graph; 12. Degree theory; Bibliography; Index.
