Summary: Stephen Simons
Minimax and Monotonicity
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Table of Contents
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Chapter I. Functional analytic preliminaries
1. The Hahn--Banach and Mazur--Orlicz theorems . . . . . . . . . 13
2. Convex, concave and a#ne functions . . . . . . . . . . . . . . . . . . . . 15
3. The minimax theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
4. The dual and bidual of a Banach space . . . . . . . . . . . . . . . . . . 18
5. The minimax criterion for weak compactness in a
Banach space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
6. Four examples of the ``minimax technique'' --- Fenchel
duality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
7. The perfect square trick and the fg--theorem . . . . . . . . . . . 27

Source: Akhmedov, Azer - Department of Mathematics, University of California at Santa Barbara

Collections: Mathematics