Overview
- Includes supplementary material: sn.pub/extras
Part of the book series: Lecture Notes in Mathematics (LNM)
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Table of contents (11 chapters)
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Front Matter
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Back Matter
Keywords
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)
Authors and Affiliations
Bibliographic Information
Book Title: From Hahn-Banach to Monotonicity
Authors: Stephen Simons
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/978-1-4020-6919-2
Publisher: Springer Dordrecht
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media B.V. 2008
Softcover ISBN: 978-1-4020-6918-5Published: 13 February 2008
eBook ISBN: 978-1-4020-6919-2Published: 22 February 2008
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 2
Number of Pages: XIV, 248
Additional Information: Orignally published by Springer-Verlag Heidelberg, 1998
Topics: Functional Analysis, Calculus of Variations and Optimal Control; Optimization, Operator Theory
Industry Sectors: IT & Software