Fixed point theorems and applications

Preface......Page 7
Introduction......Page 8
 Notation......Page 9
Contents......Page 14
About the Author......Page 16
Part I Fixed Point Theorems......Page 17
1 The Banach Contraction Principle......Page 18
2 The Boyd-Wong Theorem......Page 24
3 Further Extensions of the Contraction Principle......Page 27
4 Weak Contractions......Page 34
5 Contractions of ε-Type......Page 40
6 Sequences of Maps and Fixed Points......Page 48
7 Fixed Points of Non-expansive Maps......Page 51
8 The Riesz Mean Ergodic Theorem......Page 54
9 The Brouwer Fixed Point Theorem......Page 58
10 The Schauder-Tychonoff Fixed Point Theorem......Page 63
11 Further Consequences  of the Schauder-Tychonoff Theorem......Page 68
12 The Markov-Kakutani Theorem......Page 73
13 The Kakutani-Ky Fan Theorem......Page 75
Part II Some Applications......Page 81
14 The Implicit Function Theorem......Page 82
15 Location of Zeros......Page 88
16 Ordinary Differential Equations in Banach Spaces......Page 91
17 The Lax-Milgram Lemma......Page 102
18 An Abstract Elliptic Problem......Page 110
19 Semilinear Evolution Equations......Page 114
20 An Abstract Parabolic Problem......Page 122
21 The Invariant Subspace Problem......Page 129
22 Measure Preserving Maps on Compact Hausdorff Spaces......Page 133
23 Invariant Means on Semigroups......Page 136
24 Haar Measures......Page 140
25 Game Theory......Page 148
Part III Some Problems......Page 152
26 Problems......Page 153
 References......Page 166
Index......Page 169