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Record Nr. |
UNISA996466870203316 |
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Autore |
Simons Stephen |
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Titolo |
From Hahn-Banach to Monotonicity [[electronic resource] /] / by Stephen Simons |
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Pubbl/distr/stampa |
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Dordrecht : , : Springer Netherlands : , : Imprint : Springer, , 2008 |
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ISBN |
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Edizione |
[2nd ed. 2008.] |
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Descrizione fisica |
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1 online resource (XIV, 248 p.) |
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Collana |
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Lecture Notes in Mathematics, , 0075-8434 |
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Disciplina |
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Soggetti |
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Functional analysis |
Calculus of variations |
Operator theory |
Functional Analysis |
Calculus of Variations and Optimal Control; Optimization |
Operator Theory |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Original edition published as: Minimax and monotonicity. |
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Nota di bibliografia |
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Includes bibliographical references (pages [233]-238) and index. |
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Nota di contenuto |
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The Hahn-Banach-Lagrange theorem and some consequences -- Fenchel duality -- Multifunctions, SSD spaces, monotonicity and Fitzpatrick functions -- Monotone multifunctions on general Banach spaces -- Monotone multifunctions on reflexive Banach spaces -- Special maximally monotone multifunctions -- The sum problem for general Banach spaces -- Open problems -- Glossary of classes of multifunctions -- A selection of results. |
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Sommario/riassunto |
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In this new edition of LNM 1693 the essential idea is to reduce questions on monotone multifunctions to questions on convex functions. However, rather than using a “big convexification” of the graph of the multifunction and the “minimax technique”for proving the existence of linear functionals satisfying certain conditions, the Fitzpatrick function is used. The journey begins with a generalization of the Hahn-Banach theorem uniting classical functional analysis, minimax theory, Lagrange multiplier theory and convex analysis and culminates in a survey of current results on monotone multifunctions on a Banach space. The first two chapters are aimed at students interested in the development of the basic theorems of functional |
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