TY  - BOOK
AU  - 
ED  - SpringerLink (Online service)
TI  - From Hahn-Banach to Monotonicity
T2  - Lecture Notes in Mathematics,
SN  - 9781402069192
AV  - QA319-329.9 
U1  - 515.7 23
PY  - 2008///
CY  - Dordrecht
PB  - Springer Netherlands
KW  - Mathematics
KW  - Functional analysis
KW  - Operator theory
KW  - Mathematical optimization
KW  - Functional Analysis
KW  - Calculus of Variations and Optimal Control; Optimization
KW  - Operator Theory
N1  - 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; ZDB-2-SMA; ZDB-2-LNM
N2  - 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 ǣbig convexificationǥ of the graph of the multifunction and the ǣminimax techniqueǥfor 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
UR  - http://dx.doi.org/10.1007/978-1-4020-6919-2
ER  -