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From Hahn-Banach to Monotonicity

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ISBN-10: 1402069189

ISBN-13: 9781402069185

Edition: 2nd 2008

Authors: Stephen Simons

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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 & the 'minimax technique'for proving the existence of linear functionals satisfying certain conditions, the Fitzpatrick function is used.
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Book details

Edition: 2nd
Copyright year: 2008
Publisher: Springer
Publication date: 2/13/2008
Binding: Paperback
Pages: 248
Size: 6.00" wide x 9.00" long x 0.75" tall
Weight: 0.880
Language: English

The Hahn-Banach-Lagrange theorem and some consequences
The Hahn-Banach-Lagrange theorem
Applications to functional analysis
A minimax theorem
The dual and bidual of a normed space
Excess, duality gap, and minimax criteria for weak compactness
Sharp Lagrange multiplier and KKT results
Fenchel duality
A sharp version of the Fenchel Duality theorem
Fenchel duality with respect to a bilinear form - locally convex spaces
Some properties of 1/2.2
The conjugate of a sum in the locally convex case
Fenchel duality vs the conjugate of a sum
The restricted biconjugate and Fenchel-Moreau points
Surrounding sets and the dom lemma
The ⊖-theorem
The Attouch-Brezis theorem
A bivariate Attouch-Brezis theorem
Multifunctions, SSD spaces, monotonicity and Fitzpatrick functions
Multifunctions, monotonicity and maximality
Subdifferentials are maximally monotone
SSD spaces, q-positive sets and BC-functions
Maximally q-positive sets in SSD spaces
SSDB spaces
The SSD space E � E*
Fitzpatrick functions and fitzpatrifications
The maximal monotonicity of a sum
Monotone multifunctions on general Banach spaces
Monotone multifunctions with bounded range
A general local boundedness theorem
The six set theorem and the nine set theorem
D(S<sub>&varphi;</sub>) and various hulls
Monotone multifunctions on reflexive Banach spaces
Criteria for maximality, and Rockafellar's surjectivity theorem
Surjectivity and an abstract Hammerstein theorem
The Brezis-Haraux condition
Bootstrapping the sum theorem
The > six set and the > nine set theorems for pairs of multifunctions
The Brezis-Crandall-Pazy condition
Special maximally monotone multifunctions
The norm-dual of the space E � E* and <$>-functions
Subclasses of the maximally monotone multifunctions
First application of Theorem 35.8: type (D) implies type (FP)
T<sub>clb</sub>(E**), T<sub>clbn</sub>(B*) and type (ED)
Second application of Theorem 35.8: type (ED) implies type (FPV)
Final applications of Theorem 35.8: type (ED) implies strong
Strong maximality and coercivity
Type (ED) implies type (ANA) and type (BR)
The closure of the range
The sum problem and the closure of the domain
The biconjugate of a maximum and T<sub>clb</sub>(E**)
Maximally monotone multifunctions with convex graph
Possibly discontinuous positive linear operators
Subtler properties of subdifferentials
Saddle functions and type (ED)
The sum problem for general Banach spaces
Introductory comments
Voisei's theorem
Sums with normality maps
A theorem of Verona-Verona
Open problems
Glossary of classes of multifunctions
A selection of results
Subject index
Symbol index