Simons Stephen. From Hahn-Banach to Monotonicity

2nd Edition. — Springer, 2008. — 251 p. — (Lecture Notes in Mathematics 1693). — ISBN 978-1-4020-6918-5.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 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