ENGLISH

From Hahn-Banach to monotonicity

By Stephen Simons

Book information

Publisher
Springer
Year
2008
ISBN
1402069189, 9781402069185
LCC
QA329.8 .S58 2008
Open Library ID
OL18866709M
Language
english
Format
PDF
Filesize
2 MB (1903372 bytes)
Series
Lecture Notes in Mathematics 1693
Edition
2nd, exp. ed.
Pages
264\264
Library
Kolxo3
Scanned
yes
Time added
2009-07-20 03:45:11

Description

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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