Jump to ContentJump to Main Navigation
Fréchet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces (AM-179)$
Users without a subscription are not able to see the full content.

Joram Lindenstrauss, David Preiss, and Jaroslav Tier

Print publication date: 2012

Print ISBN-13: 9780691153551

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691153551.001.0001

Show Summary Details
Page of

PRINTED FROM PRINCETON SCHOLARSHIP ONLINE (www.princeton.universitypressscholarship.com). (c) Copyright Princeton University Press, 2018. All Rights Reserved. Under the terms of the licence agreement, an individual user may print out a PDF of a single chapter of a monograph in HSO for personal use (for details see www.princeton.universitypressscholarship.com/page/privacy-policy).date: 23 October 2018

Fr échet Differentiability of Real-Valued Functions

Fr échet Differentiability of Real-Valued Functions

Chapter:
(p.222) Chapter Twelve Fr échet Differentiability of Real-Valued Functions
Source:
Fréchet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces (AM-179)
Author(s):

Joram Lindenstrauss

David Preiss

Tiˇser Jaroslav

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691153551.003.0012

This chapter shows that cone-monotone functions on Asplund spaces have points of Fréchet differentiability and that the appropriate version of the mean value estimates holds. It also proves that the corresponding point of Fréchet differentiability may be found outside any given σ‎-porous set. This new result considerably strengthens known Fréchet differentiability results for real-valued Lipschitz functions on such spaces. The avoidance of σ‎-porous sets is new even in the Lipschitz case. The chapter first discusses the use of variational principles to prove Fréchet differentiability before analyzing a one-dimensional mean value problem in relation to Lipschitz functions. It shows that results on existence of points of Fréchet differentiability may be generalized to derivatives other than the Fréchet derivative.

Keywords:   cone-monotone function, Asplund space, Fréchet differentiability, mean value estimate, Lipschitz function, σ‎-porous sets, variational principles, Fréchet derivative

Princeton Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us.