Classification of Lipschitz Mappings (Chapman & Hall/CRC Monographs and Research Notes in Mathematics)

Cover
Half Title
Series Page
Title Page
Copyright Page
Contents
Preface
Authors
1. Basic Facts about Banach Spaces
	1.1. Convexity
	1.2. Dual Spaces, Reflexivity, the Weak, and Weak∗ Topologies
2. Mean Lipschitzian Mappings
	2.1. The Lipschitz Condition
	2.2. The Mean Lipschitz Condition
		2.2.1. Nonexpansive and mean nonexpansive mappings
		2.2.2. Contractions and mean contractions
	2.3. Notes and Comments
3. On the Lipschitz Constants for Iterates of Mean Lipschitzian Mappings
	3.1. The Case of (α1, α2)-nonexpansive Mappings
	3.2. The Case of (α1, α2)-Lipschitzian Mappings for k > 0
	3.3. The Case of (α1, . . . , αn)-Lipschitzian Mappings for k > 0
	3.4. Asymptotic Behavior of Lipschitz Constants
		3.4.1. More examples
	3.5. A Bound for Nonlinear Spectral Radius
4. Some Applications
	4.1. Real Moving Averages
		4.1.1. Arithmetic moving averages
		4.1.2. Harmonic moving averages
		4.1.3. Geometric moving averages
	4.2. Moving Averages in Banach Spaces
	4.3. A Fibonacci Approach for Solving Polynomials in Banach Algebras
		4.3.1. Solving polynomials: the real case
		4.3.2. Solving polynomials: the Banach algebra case
	4.4. Computer Experiments
	4.5. Isometric Conditions and Some Generalizations
		4.5.1. Mean isometries are isometries
		4.5.2. Affine combination mappings
		4.5.3. A contraction mapping theorem
		4.5.4. Lipschitz constants of iterates revisited
5. Nonexpansive Mappings in Banach Spaces
	5.1. Classical Results
	5.2. The Asymptotic Center Technique
	5.3. Minimal Invariant Sets and Normal Structure
	5.4. More about Fixed Point Property in ℓ1
		5.4.1. Goebel–Kuczumow sets
		5.4.2. Weak∗ fixed point property in ℓ1
		5.4.3. Notes and Comments
	5.5. The Fixed Point Property for Uniformly Lipschitzian Mappings
6. Fixed Point Property for Mean Nonexpansive Mappings
	6.1. The Goebel–Japón Theorems
	6.2. Fixed Point Results Using the Lifshitz Constant
	6.3. On the Structure of the Fixed Points Set
	6.4. The Demiclosedness Principle for Mean Nonexpansive Mappings
		6.4.1. Uniform Convexity
		6.4.2. Opial’s Property
	6.5. Some Applications of the Demiclosedness Principle for Mean Nonexpansive Mappings
		6.5.1. Fixed point results
		6.5.2. A weak convergence theorem
		6.5.3. Results for averaging with the identity
		6.5.4. Affine mean nonexpansive mappings
7. Mean Lipschitzian Mappings with k > 1
	7.1. Losing Compactness in Brouwer’s Fixed Point Theorem
	7.2. Retracting onto Balls in Banach Spaces
	7.3. Minimal Displacement
	7.4. Optimal Retractions
	7.5. Generalized Characteristics of Minimal Displacement
Bibliography
Index