From Hahn-Banach to Monotonicity / Lecture Notes in Mathematics (PDF)
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...
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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 analysis, which leads painlessly to the theory of minimax theorems, convex Lagrange multiplier theory and convex analysis. The remaining five chapters are useful for those who wish to learn about the current research on monotone multifunctions on (possibly non reflexive) Banach space.
- Autor: Stephen Simons
- 2008, 2nd ed. 2008, 248 Seiten, Englisch
- Verlag: Springer-Verlag GmbH
- ISBN-10: 1402069197
- ISBN-13: 9781402069192
- Erscheinungsdatum: 22.02.2008
Abhängig von Bildschirmgröße und eingestellter Schriftgröße kann die Seitenzahl auf Ihrem Lesegerät variieren.
- Dateiformat: PDF
- Größe: 3.33 MB
- Mit Kopierschutz
- Vorlesefunktion
From the reviews of the second edition:
"Like the first edition it is cleanly, indeed elegantly, written and singularly free of even minor infelicities. … The book has seven core chapters … . In conclusion, I highly recommend this book as a resource to anyone interested in learning, teaching or applying the modern abstract theory of monotone multifunctions." (J. Borwein, Mathematical Reviews, Issue 2008 k)
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