Buch, Englisch, Band 1693, 248 Seiten, Format (B × H): 157 mm x 235 mm, Gewicht: 407 g
Reihe: Lecture Notes in Mathematics
Buch, Englisch, Band 1693, 248 Seiten, Format (B × H): 157 mm x 235 mm, Gewicht: 407 g
Reihe: Lecture Notes in Mathematics
ISBN: 978-1-4020-6918-5
Verlag: Springer
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.
Zielgruppe
Research
Autoren/Hrsg.
Fachgebiete
- Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
- Mathematik | Informatik Mathematik Operations Research Spieltheorie
- Mathematik | Informatik Mathematik Mathematische Analysis Variationsrechnung
- Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik
Weitere Infos & Material
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.
