From Hahn-Banach to monotonicity

Stephen Simons1402069189, 9781402069185

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.

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Table of contents :
Cover……Page 1
Lecture Notes in Mathematics 1693……Page 2
From Hahn-Banach to Monotonicity……Page 3
Preface……Page 6
Table of Contents……Page 9
Introduction……Page 26
I The Hahn-Banach-Lagrange theorem and some consequences……Page 39
II Fenchel duality……Page 64
III Multifunctions, SSD spaces, monotonicity and Fitzpatrick functions……Page 93
IV Monotone multifunctions on general Banach spaces……Page 128
V Monotone multifunctions on reflexive Banach spaces……Page 137
VI Special maximally monotone multifunctions……Page 159
VII The sum problem for general Banach spaces……Page 216
VIII Open problems……Page 221
IX Glossary of classes of multifunctions……Page 223
X A selection of results……Page 225
References……Page 250
Subject Index……Page 256
Lecture Notes in Mathematics……Page 261