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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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Distinct differentiable functions may share the same Clarke subdifferential at all points
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by J. M. Borwein and Xianfu Wang PDF
Proc. Amer. Math. Soc. 125 (1997), 807-813 Request permission

Abstract:

We construct, using Zahorski’s Theorem, two everywhere differentiable real–valued Lipschitz functions differing by more than a constant but sharing the same Clarke subdifferential and the same approximate subdifferential.
References
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Additional Information
  • J. M. Borwein
  • Affiliation: Department of Mathematics and Statistics, Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6
  • Email: jborwein@cecm.sfu.ca
  • Xianfu Wang
  • Affiliation: Department of Mathematics and Statistics, Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6
  • MR Author ID: 601305
  • Email: xwang@cecm.sfu.ca
  • Received by editor(s): July 13, 1995
  • Received by editor(s) in revised form: September 8, 1995
  • Additional Notes: The first author’s research supported by NSERC and the Shrum Endowment at Simon Fraser University.
  • Communicated by: J. Marshall Ash
  • © Copyright 1997 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 125 (1997), 807-813
  • MSC (1991): Primary 49J52; Secondary 26A27, 26A16
  • DOI: https://doi.org/10.1090/S0002-9939-97-03654-X
  • MathSciNet review: 1363449