Geometry of Banach Spaces, Duality Mappings and Nonlinear Problems

Inhaltsverzeichnis

• I. Subdifferentiability and Duality Mappings.
• § 1. Generalities on convex functions.
• § 2. The subdifferential and the conjugate of a convex function.
• § 3. Smooth Banach spaces.
• § 4. Duality mappings on Banach spaces.
• § 5. Positive duality mappings.
• Exercises.
• Bibliographical comments.
• II Characterizations of Some Classes of Banach Spaces by Duality Mappings.
• § 1. Strictly convex Banach spaces.
• § 2. Uniformly convex Banach spaces.
• § 3. Duality mappings in reflexive Banach spaces.
• § 4. Duality mappings in LP-spaces.
• § 5. Duality mappings in Banach spaces with the property (h) and (?)1.
• III Renorming of Banach Spaces.
• § 1. Classical renorming results.
• § 2. Lindenstrauss’ and Trojanski’s Theorems.
• IV On the Topological Degree in Finite and Infinite Dimensions.
• § 1. Brouwer’s degree.
• § 2. Browder-Petryshyn’s degree for A-proper mappings.
• § 3. P-compact mappings.
• V Nonlinear Monotone Mappings.
• § 1. Demicontinuity and hemicontinuity for monotone operators.
• § 2. Monotone and maximal monotone mappings.
• § 3. The role of the duality mapping in surjectivity and maximality problems.
• § 4. Again on subdifferentials of convex functions.
• VI Accretive Mappings and Semigroups of Nonlinear Contractions.
• § 1. General properties of maximal accretive mappings.
• § 2. Semigroups of nonlinear contractions in uniformly convex Banach spaces.
• § 3. The exponential formula of Crandall-Liggett.
• § 4. The abstract Cauchy problem for accretive mappings.
• § 5. Semigroups of nonlinear contractions in Hilbert spaces.
• § 6. The inhomogeneous case.
• References.