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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Differentiability of cone-monotone functions on separable Banach space
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by Jonathan M. Borwein, James V. Burke and Adrian S. Lewis PDF
Proc. Amer. Math. Soc. 132 (2004), 1067-1076 Request permission

Abstract:

Motivated by applications to (directionally) Lipschitz functions, we provide a general result on the almost everywhere Gâteaux differentiability of real-valued functions on separable Banach spaces, when the function is monotone with respect to an ordering induced by a convex cone with non-empty interior. This seemingly arduous restriction is useful, since it covers the case of directionally Lipschitz functions, and necessary. We show by way of example that most results fail more generally.
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Additional Information
  • Jonathan M. Borwein
  • Affiliation: Department of Mathematics, Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6
  • Email: jborwein@cecm.sfu.ca
  • James V. Burke
  • Affiliation: Department of Mathematics, University of Washington, Box 354350, Seattle, Washington 98195-4350
  • Email: burke@math.washington.edu
  • Adrian S. Lewis
  • Affiliation: Department of Mathematics, Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6
  • Email: aslewis@cecm.sfu.ca
  • Received by editor(s): April 11, 2002
  • Received by editor(s) in revised form: November 19, 2002
  • Published electronically: July 14, 2003
  • Additional Notes: The first author’s research was supported by NSERC and by the Canada Research Chair Programme. The second author’s research was supported by NSF DMS-9971852 & NIH P41-RR-12609. The third author’s research was supported by NSERC
  • Communicated by: N. Tomczak-Jaegermann
  • © Copyright 2003 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 132 (2004), 1067-1076
  • MSC (2000): Primary 26B25; Secondary 90C29
  • DOI: https://doi.org/10.1090/S0002-9939-03-07149-1
  • MathSciNet review: 2045422