Geometry of Banach Spaces, Duality Mappings and Nonlinear Problems [Paperback]

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 Trojanskis Theorems.- Exercises.- Bibliographical comments.- IV On the Topological Degree in Finite and Infinite Dimensions.- ? 1. Brouwers degree.- ? 2. Browder-Petryshyns 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.Springer Book Archives