Contents 

1. 
Preliminaries 

1.1 Topological Spaces 

1.2 Banach Spaces and Hilbert Spaces 

1.3 Lower Semicontinuous and Convex Functions 

1.4 Banach Limits and Invariant Means 
2. 
Fixed Point Theory in Metric Spaces 

2.1 Existence Theorems in Complete Metric
Spaces 

2.2 wDistances on Metric Spaces 

2.3 Characterizations of Metric Completeness 
3. 
Fixed Point Theory in Hilbert Spaces 

3.1 Some Properties of Hilbert Spaces 

3.2 Baillon's Nonlinear Ergodic Theorem 

3.3 Fixed Point Theorem for Nonexpansive
Semigroups 

3.4 Generalized Nonlinear Ergodic Theorems 

3.5 Some Nonlinear Ergodic Theorems 

3.6 Fixed Point Theorems for Lipschitzian
Semigroups 
4. 
Geometry of Banach Spaces 

4.1 Convexity of Banach Spaces 

4.2 Duality Mappings 

4.3 Differentiability of Norms 

4.4 Nonexpansive Mappings in Banach Spaces 

4.5 Fixed Point Theorems for Nonexpansive
Families 

4.6 Accretive Operators 
5. 
Convergence Theorems in Banach Spaces 

5.1 The Behavior or Resolvents Jr when r > oo 

5.2 The Behaviro or Resolvents Jr when r > 0 

5.3 Nonlinear Ergodic Theorems in Banach
Spaces 

5.4 The Problem of Image Recovery 

5.5 Ergodic Theorems for Linear Operators 
6. 
Fixed Point Theory in Topological Vector
Spaces 

6.1 FanBrowder's Fixed Point Theorem 

6.2 Ceneralized Fixed Point Theorems 

6.3 Minimax Theorems 

6.4 MazurOrlicz Theorem 

6.5 Separation and Best Approximation Theorems 
7. 
Some Applications 

7.1 Variational Inequalities 

7.2 Cores of Games 

7.3 Applications to Linear Operators 

7.4 Linear Inequalities and Minimum Norm
Problems 

