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  • © 1989

Convex Functions, Monotone Operators and Differentiability

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

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Table of contents (8 chapters)

  1. Front Matter

    Pages I-IX
  2. Convex functions on real Banach spaces

    • Robert R. Phelps
    Pages 1-16
  3. Lower semicontinuous convex functions

    • Robert R. Phelps
    Pages 40-63
  4. Gateaux differentiability spaces

    • Robert R. Phelps
    Pages 90-96
  5. Notes and Remarks

    • Robert R. Phelps
    Pages 104-107
  6. Back Matter

    Pages 108-118

About this book

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

  • Department of Mathematics GN-50, University of Washington, Seattle, USA

    Robert R. Phelps

Bibliographic Information

  • Book Title: Convex Functions, Monotone Operators and Differentiability

  • Authors: Robert R. Phelps

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/978-3-662-21569-2

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1989

  • eBook ISBN: 978-3-662-21569-2Published: 11 December 2013

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: XII, 120

  • Topics: Analysis

Buying options

eBook USD 74.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions