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On the Construction of H\"older and Proximal Subderivatives

Borwein, Jonathan M. and Girgensohn, Roland and Wang, Shawn Xianfu (1998) On the Construction of H\"older and Proximal Subderivatives. Canadian Bulletin of Mathematics, 41 . pp. 497-507.

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      Abstract

      We construct Lipschitz functions such that for all $s>0$ they are $s$--H\"older, and so proximally, subdifferentiable only on dyadic rationals and nowhere else. As applications we construct Lipschitz functions with prescribed H\"older and approximate subderivatives.

      Item Type: Article
      Additional Information: pubdom FALSE
      Uncontrolled Keywords: Lipschitz function, Holder subdifferential, proximal subdifferential, approximate subdifferential, symmetric subdifferential, Holder smooth, dyadic rationals
      Subjects: 49-xx Calculus of variations and optimal control; optimization > 49Jxx Existence theories
      26-xx Real functions > 26Axx Functions of one variable
      Faculty: UNSPECIFIED
      Depositing User: Users 1 not found.
      Date Deposited: 25 Nov 2003
      Last Modified: 20 Sep 2014 20:06
      URI: https://docserver.carma.newcastle.edu.au/id/eprint/186

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