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On the construction of Hölder and Proximal Subderivatives

  Published:1998-12-01
 Printed: Dec 1998
  • J. M. Borwein
  • R. Girgensohn
  • Xianfu Wang
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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.
Keywords: Lipschitz functions, Hölder subdifferential, proximal subdifferential, approximate subdifferential, symmetric subdifferential, Hölder smooth, dyadic rationals Lipschitz functions, Hölder subdifferential, proximal subdifferential, approximate subdifferential, symmetric subdifferential, Hölder smooth, dyadic rationals
MSC Classifications: 49J52, 26A16, 26A24 show english descriptions Nonsmooth analysis [See also 46G05, 58C50, 90C56]
Lipschitz (Holder) classes
Differentiation (functions of one variable): general theory, generalized derivatives, mean-value theorems [See also 28A15]
49J52 - Nonsmooth analysis [See also 46G05, 58C50, 90C56]
26A16 - Lipschitz (Holder) classes
26A24 - Differentiation (functions of one variable): general theory, generalized derivatives, mean-value theorems [See also 28A15]
 

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