Minimax and Monotonicity

1. Auflage 1998
ISBN: 978-3-540-64755-3
Verlag: Springer

Buch, Englisch, Band 1693, 172 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 471 g

Reihe: Lecture Notes in Mathematics

Focussing on the theory (both classical and recent) of monotone multifunctions on a (possibly nonreflexive) Banach space, this book looks at the big convexification of a multifunction; convex functions associated with a multifunction; minimax theorems as a tool in functional analysis and convex analysis. It includes new results on the existence of continuous linear functionals; the conjugates, biconjugates and subdifferentials of convex lower semicontinuous functions, Fenchel duality; (possibly unbounded) positive linear operators from a Banach space into its dual; the sum of maximal monotone operators, and a list of open problems. The reader is expected to know basic functional analysis and calculus of variations, including the Bahn-Banach theorem, Banach-Alaoglu theorem, Ekeland's variational principle.

Zielgruppe

Research

Autoren/Hrsg.

Simons, Stephen

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Computeranwendungen in der Mathematik
• Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle

Inhaltsverzeichnis

Functional analytic preliminaries.- Multifunctions.- A digression into convex analysis.- General monotone multifunctions.- The sum problem for reflexive spaces.- Special maximal monotone multifunctions.- Subdifferentials.- Discontinuous positive linear operators.- The sum problem for general banach spaces.- Open problems.