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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
MathSciNet review: 1363449
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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.


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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: http://dx.doi.org/10.1090/S0002-9939-97-03654-X
PII: S 0002-9939(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