Ebook: Minimax and Monotonicity

Focussing on the theory (both classical and recent) of monotone multifunctions on a (possibly nonreflexive) Banach space, this book looks at the big convexification of a multifunction; convex functions associated with a multifunction; minimax theorems as a tool in functional analysis and convex analysis. It includes new results on the existence of continuous linear functionals; the conjugates, biconjugates and subdifferentials of convex lower semicontinuous functions, Fenchel duality; (possibly unbounded) positive linear operators from a Banach space into its dual; the sum of maximal monotone operators, and a list of open problems. The reader is expected to know basic functional analysis and calculus of variations, including the Bahn-Banach theorem, Banach-Alaoglu theorem, Ekeland's variational principle.

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Focussing on the theory (both classical and recent) of monotone multifunctions on a (possibly nonreflexive) Banach space, this book looks at the big convexification of a multifunction; convex functions associated with a multifunction; minimax theorems as a tool in functional analysis and convex analysis. It includes new results on the existence of continuous linear functionals; the conjugates, biconjugates and subdifferentials of convex lower semicontinuous functions, Fenchel duality; (possibly unbounded) positive linear operators from a Banach space into its dual; the sum of maximal monotone operators, and a list of open problems. The reader is expected to know basic functional analysis and calculus of variations, including the Bahn-Banach theorem, Banach-Alaoglu theorem, Ekeland's variational principle.
Content:
Front Matter....Pages -
Introduction....Pages 1-11
Functional analytic preliminaries....Pages 13-28
Multifunctions....Pages 29-41
A digression into convex analysis....Pages 43-51
General monotone multifunctions....Pages 53-73
The sum problem for reflexive spaces....Pages 75-95
Special maximal monotone multifunctions....Pages 97-109
Subdifferentials....Pages 111-139
Discontinuous positive linear operators....Pages 141-151
The sum problem for general banach spaces....Pages 153-161
Open problems....Pages 163-164
Back Matter....Pages -

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Focussing on the theory (both classical and recent) of monotone multifunctions on a (possibly nonreflexive) Banach space, this book looks at the big convexification of a multifunction; convex functions associated with a multifunction; minimax theorems as a tool in functional analysis and convex analysis. It includes new results on the existence of continuous linear functionals; the conjugates, biconjugates and subdifferentials of convex lower semicontinuous functions, Fenchel duality; (possibly unbounded) positive linear operators from a Banach space into its dual; the sum of maximal monotone operators, and a list of open problems. The reader is expected to know basic functional analysis and calculus of variations, including the Bahn-Banach theorem, Banach-Alaoglu theorem, Ekeland's variational principle.
Content:
Front Matter....Pages -
Introduction....Pages 1-11
Functional analytic preliminaries....Pages 13-28
Multifunctions....Pages 29-41
A digression into convex analysis....Pages 43-51
General monotone multifunctions....Pages 53-73
The sum problem for reflexive spaces....Pages 75-95
Special maximal monotone multifunctions....Pages 97-109
Subdifferentials....Pages 111-139
Discontinuous positive linear operators....Pages 141-151
The sum problem for general banach spaces....Pages 153-161
Open problems....Pages 163-164
Back Matter....Pages -
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