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On the Construction of Hölder and Proximal Subderivatives

Published online by Cambridge University Press:  20 November 2018

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.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1998

References

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