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On the Construction of Hölder and Proximal Subderivatives

Published online by Cambridge University Press:  20 November 2018

J. M. Borwein ,
R. Girgensohn  and
Xianfu Wang
J. M. Borwein
Affiliation:
Department of Mathematics and Statistics Simon Fraser University Burnaby, BC V5A 1S6, email: jborwein@cecm.sfu.ca
R. Girgensohn
Affiliation:
GSF-Forschungszentrum Institut für Biomathematik und Biometrie Postfach 1129 85758 Neuherberg Germany, email: girgen@janus.gsf.de
Xianfu Wang
Affiliation:
Department of Mathematics and Statistics Simon Fraser University Burnaby, BC V5A 1S6, email: xwang@cecm.sfu.ca
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Abstract

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

Keywords

49J5226A1626A24Lipschitz functionsHölder subdifferentialproximal subdifferentialapproximate subdifferentialsymmetric subdifferentialHölder smoothdyadic rationals
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 41 , Issue 4 , 01 December 1998 , pp. 497 - 507
Copyright
Copyright © Canadian Mathematical Society 1998

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