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Distinct differentiable functions may share
the same Clarke subdifferential at all points


Authors: J. M. Borwein and Xianfu Wang
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
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Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

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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
Email: xwang@cecm.sfu.ca

DOI: https://doi.org/10.1090/S0002-9939-97-03654-X
Keywords: Lipschitz function, differentiability, integrability, generalized derivative, Clarke subdifferential, approximate continuity, metric density
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
Article copyright: © Copyright 1997 American Mathematical Society

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