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Convex Functions, Monotone Operators and Differentiability

  • Robert R. Phelps

Part of the Lecture Notes in Mathematics book series (LNM, volume 1364)

Table of contents

  1. Front Matter
    Pages I-IX
  2. Robert R. Phelps
    Pages 1-16
  3. Robert R. Phelps
    Pages 40-63
  4. Robert R. Phelps
    Pages 90-96
  5. Robert R. Phelps
    Pages 104-107
  6. Back Matter
    Pages 108-118

About this book

Introduction

These notes start with an introduction to the differentiability of convex functions on Banach spaces, leading to the study of Asplund spaces and their intriguing relationship to monotone operators (and more general set-values maps) and Banach spaces with the Radon-Nikodym property. While much of this is classical, some of it is presented using streamlined proofs which were not available until recently. Considerable attention is paid to contemporary results on variational principles and perturbed optimization in Banach spaces, exhibiting their close connections with Asplund spaces. An introductory course in functional analysis is adequate background for reading these notes which can serve as the basis for a seminar of a one-term graduate course. There are numerous excercises, many of which form an integral part of the exposition.

Keywords

banach spaces functional analysis integral

Authors and affiliations

  • Robert R. Phelps
    • 1
  1. 1.Department of Mathematics GN-50University of WashingtonSeattleUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-21569-2
  • Copyright Information Springer-Verlag Berlin Heidelberg 1989
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-50735-2
  • Online ISBN 978-3-662-21569-2
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site
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