Lecture Notes in Mathematics

From Hahn-Banach to Monotonicity

Authors: Simons, Stephen

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About this book

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.

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)


Table of contents (11 chapters)

Buy this book

eBook $44.99
price for USA in USD (gross)
  • ISBN 978-1-4020-6919-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $59.99
price for USA in USD
  • ISBN 978-1-4020-6918-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
From Hahn-Banach to Monotonicity
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
1693
Copyright
2008
Publisher
Springer Netherlands
Copyright Holder
Springer Science+Business Media B.V.
eBook ISBN
978-1-4020-6919-2
DOI
10.1007/978-1-4020-6919-2
Softcover ISBN
978-1-4020-6918-5
Series ISSN
0075-8434
Edition Number
2
Number of Pages
XIV, 248
Additional Information
Orignally published by Springer-Verlag Heidelberg, 1998
Topics