Geometry of Banach Spaces, Duality Mappings and Nonlinear Problems

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.- Exercises.- Bibliographical comments.- III Renorming of Banach Spaces.- § 1. Classical renorming results.- § 2. Lindenstrauss’ and Trojanski’s Theorems.- Exercises.- Bibliographical comments.- 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.- Exercises.- Bibliographical comments.- 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.- Exercises.- Bibliographical comments.- 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.- Exercises.- Bibliographical comments.- References.