Author | Cioranescu, Ioana. author |
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Title | Geometry of Banach Spaces, Duality Mappings and Nonlinear Problems [electronic resource] / by Ioana Cioranescu |
Imprint | Dordrecht : Springer Netherlands, 1990 |
Connect to | http://dx.doi.org/10.1007/978-94-009-2121-4 |
Descript | XIV, 260 p. online resource |
I. Subdifferentiability and Duality Mappings -- ยง 1. Generalities on convex functions -- ยง 2. The subdifferential and the conjugate of a convex function -- ยง 3. Smooth Banach spaces -- ยง 4. Duality mappings on Banach spaces -- ยง 5. Positive duality mappings -- Exercises -- Bibliographical comments -- II Characterizations of Some Classes of Banach Spaces by Duality Mappings -- ยง 1. Strictly convex Banach spaces -- ยง 2. Uniformly convex Banach spaces -- ยง 3. Duality mappings in reflexive Banach spaces -- ยง 4. Duality mappings in LP-spaces -- ยง 5. Duality mappings in Banach spaces with the property (h) and (?)1 -- Exercises -- Bibliographical comments -- III Renorming of Banach Spaces -- ยง 1. Classical renorming results -- ยง 2. Lindenstraussโ and Trojanskiโs Theorems -- Exercises -- Bibliographical comments -- IV On the Topological Degree in Finite and Infinite Dimensions -- ยง 1. Brouwerโs degree -- ยง 2. Browder-Petryshynโs degree for A-proper mappings -- ยง 3. P-compact mappings -- Exercises -- Bibliographical comments -- V Nonlinear Monotone Mappings -- ยง 1. Demicontinuity and hemicontinuity for monotone operators -- ยง 2. Monotone and maximal monotone mappings -- ยง 3. The role of the duality mapping in surjectivity and maximality problems -- ยง 4. Again on subdifferentials of convex functions -- Exercises -- Bibliographical comments -- VI Accretive Mappings and Semigroups of Nonlinear Contractions -- ยง 1. General properties of maximal accretive mappings -- ยง 2. Semigroups of nonlinear contractions in uniformly convex Banach spaces -- ยง 3. The exponential formula of Crandall-Liggett -- ยง 4. The abstract Cauchy problem for accretive mappings -- ยง 5. Semigroups of nonlinear contractions in Hilbert spaces -- ยง 6. The inhomogeneous case -- Exercises -- Bibliographical comments -- References