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© 2008

From Hahn-Banach to Monotonicity

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Part of the Lecture Notes in Mathematics book series (LNM, volume 1693)

About this book

Introduction

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.

Keywords

Hahn-Banach-Lagrange theorem Lagrange multipliers convex analysis functional analysis monotone multifunctions topologies on the bidual of a Banach space

Authors and affiliations

  1. 1.University of California93105-3080Santa BarbaraUSA

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Reviews

From the reviews of the second edition:

"Like the first edition it is cleanly, indeed elegantly, written and singularly free of even minor infelicities. … The book has seven core chapters … . In conclusion, I highly recommend this book as a resource to anyone interested in learning, teaching or applying the modern abstract theory of monotone multifunctions." (J. Borwein, Mathematical Reviews, Issue 2008 k)