Minimax and monotonicity / Stephen Simons
Type de document : Livre numériqueCollection : Lecture notes in mathematics, 1693Langue : anglais.Éditeur : Berlin : Springer, 1998ISBN: 9783540647553.ISSN: 1617-9692.Sujet MSC : 47H04, Operator theory - Nonlinear operators and their properties, Set-valued operators49J35, Existence theories in calculus of variations and optimal control, Existence of solutions for minimax problems
47H05, Operator theory - Nonlinear operators and their properties, Monotone operators and generalizations
49J53, Existence theories in calculus of variations and optimal control, Set-valued and variational analysisEn-ligne : Springerlink | Zentralblatt | MathSciNet
This book puts together a number of recent results about monotone multifunctions on Banach spaces and their relations with minimax maximal monotonicity, and other related subjects. Maximal monotonicity is systematically used in the study of several subjects presented in this book.
The content of this book is the following: 1. Functional-analytic preliminaries; 2. Multifunctions; 3. A digression into convex analysis; 4. General monotone multifunctions; 5. The sum problem for reflexive spaces; 6. Special maximal monotone multifunctions; 7. Subdifferentials; 8. Discontinuous positive linear operators; 9. The sum problem for general Banach spaces; 10. Open problems.
Through this book, the reader is in contact with the most important recent results about monotonicity. The proofs are clear and the text is pleasant to read. This book is good material for a graduate course. (MathSciNet)
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