Fixed Point Theory and Applications

This book provides a clear exposition of the flourishing field of fixed point theory.

Ravi P. Agarwal (Author), Maria Meehan (Author), Donal O'Regan (Author)

9780521802505, Cambridge University Press

Hardback, published 22 March 2001

184 pages, 95 exercises
22.9 x 15.2 x 1.4 cm, 0.44 kg

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.

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.

Subject Areas: Probability & statistics [PBT], Calculus & mathematical analysis [PBK]