Fixed Point Theory and Applications

ISBN-13: 9780521802505 / Angielski / Twarda / 2001 / 184 str.

Ravi P. Agarwal; Maria Meehan; Donal O'Regan

Opis

This clear exposition of the flourishing field of fixed point theory, an important tool in the fields of differential equations and functional equations, starts from the basics of Banach's contraction theorem and develops most of the main results and techniques. The book explores many applications of the theory to analysis, with topological considerations playing a crucial role. 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.

Spis treści

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.