From Hahn-Banach to Monotonicity

• Main Author: Simons, Stephen (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Dordrecht : Springer Netherlands, 2008.
• Series: Lecture Notes in Mathematics, 1693
• Subjects: Mathematics.; Functional analysis.; Operator theory.; Calculus of variations.; Functional Analysis.; Calculus of Variations and Optimal Control; Optimization.; Operator Theory.

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 satis...

Table of Contents:

• 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.