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Distinct Differentiable Functions May Share the Same Clarke Subdifferential at All Points

Borwein, Jonathan M. and Wang, Shawn Xianfu (1997) Distinct Differentiable Functions May Share the Same Clarke Subdifferential at All Points. Proceedings of the American Mathematical Society, 125 (3). pp. 807-813. ISSN 0002-9939

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      Abstract

      We construct, using Zahorski's Theorem, two everywhere differentiable real Lipschitz functions differing by more than a constant but sharing the same Clarke subdifferential and the same approximate subdifferential. ln other words,``differentiability does not force integrability''.

      Item Type: Article
      Additional Information: pubdom FALSE
      Uncontrolled Keywords: Lipschitz function, differentiability, integrability, generalized derivative, Clarke subdifferential, approximate continuity, metric density
      Subjects: 26-xx Real functions > 26Axx Functions of one variable
      49-xx Calculus of variations and optimal control; optimization > 49Jxx Existence theories
      Faculty: UNSPECIFIED
      Depositing User: Users 1 not found.
      Date Deposited: 17 Nov 2003
      Last Modified: 13 Sep 2014 21:47
      URI: https://docserver.carma.newcastle.edu.au/id/eprint/112

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