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Convex Functions, Monotone Operators and Differentiability
     

Convex Functions, Monotone Operators and Differentiability

by Robert R. Phelps, D. McIntyre (Illustrator)
 

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The improved and expanded second edition contains expositions of some major results which have been obtained in the years since the 1st edition.
Theaffirmative answer by Preiss of the decades old question of whether a Banachspace with an equivalent Gateaux differentiable norm is a weak Asplund space.
The startlingly simple proof by Simons of Rockafellar's

Overview

The improved and expanded second edition contains expositions of some major results which have been obtained in the years since the 1st edition.
Theaffirmative answer by Preiss of the decades old question of whether a Banachspace with an equivalent Gateaux differentiable norm is a weak Asplund space.
The startlingly simple proof by Simons of Rockafellar's fundamental maximal monotonicity theorem for subdifferentials of convex functions.
The exciting new version of the useful Borwein-Preiss smooth variational principle due to Godefroy, Deville and Zizler.
The material is accessible to students who have had a course in Functional Analysis; indeed, the first edition has been used in numerous graduate seminars. Starting with convex functions on the line, it leads to interconnected topics in convexity, differentiability and subdifferentiability of convex functions in Banach spaces, generic continuity of monotone operators, geometry of Banach spaces and the
Radon-Nikodym property, convex analysis, variational principles and perturbed optimization.
While much of this is classical, streamlined proofs found more recently are given in many instances. There are numerous exercises, many of which form an integral part of the exposition.

Product Details

ISBN-13:
9783540567158
Publisher:
Springer Berlin Heidelberg
Publication date:
09/10/1993
Series:
Lecture Notes in Mathematics Series , #1364
Edition description:
2nd ed. 1993
Pages:
120
Product dimensions:
6.14(w) x 9.21(h) x 0.28(d)

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