Fixed point theorems

Contents......Page 0003_0001.djvu
Preface......Page 0005_0001.djvu
Symbols used......Page 0006_0001.djvu
1.1 Introduction......Page 0007_0001.djvu
1.2. The contraction mapping theorem......Page 0008_0001.djvu
1.3 The Cauchy-Lipschitz theorem......Page 0009_0001.djvu
1.4 Implicit functions:......Page 0011_0001.djvu
1.5 Other applications......Page 0013_0001.djvu
2.1 The fixed point property......Page 0015_0001.djvu
2.2 Other proofs of Brouwer\'s theorem......Page 0018_0001.djvu
2.3 Extensions to infinite-dimensional spaces......Page 0019_0001.djvu
2.4 Kakutani\'s example......Page 0021_0001.djvu
3.1 Compact contractible sets......Page 0024_0001.djvu
3.2 Pathology......Page 0026_0001.djvu
4.1 Schauder\'s second theorem......Page 0031_0001.djvu
4.2 Rothe\'s theorem......Page 0032_0001.djvu
4.3 Continuation theorems......Page 0034_0001.djvu
4.4 Krasnoselskii\'s theorem......Page 0037_0001.djvu
4.5 Locally convex spaces......Page 0038_0001.djvu
5.1 Bounded convex sets......Page 0041_0001.djvu
5.2 Various......Page 0044_0001.djvu
6.1 Methods available......Page 0047_0001.djvu
6.2 Ordinary D.E.s......Page 0049_0001.djvu
6.3 Two-point boundary conditions......Page 0052_0001.djvu
6.4 Periodic solutions......Page 0053_0001.djvu
6.5 Partial D.E.s: use of a Green\'s function......Page 0055_0001.djvu
6.6 The linearisation trick for partial D.E.s......Page 0056_0001.djvu
6.7 The methods of Leray-Schauder and Schaefer......Page 0057_0001.djvu
7.1 Commuting mappings......Page 0059_0001.djvu
7.2 Downward induction......Page 0063_0001.djvu
7.3 Groups and semigroups of mappings......Page 0064_0001.djvu
8.1 Almost periodic functions......Page 0068_0001.djvu
8.2 Banach limits......Page 0069_0001.djvu
8.3 Haar measure......Page 0071_0001.djvu
8.4 Day\'s fixed point theorem......Page 0073_0001.djvu
9.1 Kakutani\'s theorem......Page 0074_0001.djvu
9.2 Generalisations......Page 0076_0001.djvu
9.3 Theory of games......Page 0078_0001.djvu
10.1 The rotation of a vector field......Page 0081_0001.djvu
10.2 The degree for mappings of spheres......Page 0083_0001.djvu
10.3 The degree for mappings of open sets......Page 0085_0001.djvu
10.4 The index and Lefschetz number......Page 0089_0001.djvu
11 FURTHER TOPICS......Page 0091_0001.djvu
Bibliography......Page 0093_0001.djvu
Index......Page 0099_0001.djvu