Distinct differentiable functions may share the same Clarke subdifferential at all points

Borwein, J. M.; Wang, Xianfu

Distinct differentiable functions may share the same Clarke subdifferential at all points

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posted on 2025-05-08, 14:23 authored by J. M. Borwein, Xianfu Wang

We construct, using Zahorski's Theorem, two everywhere differentiable real-valued Lipschitz functions differing by more than a constant but sharing the same Clarke subdifferential and the same approximate subdifferential.

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DOI - Is published in https://doi.org/10.1090/S0002-9939-97-03654-X
2.
ISSN - Is version of https://portal.issn.org/resource/ISSN/0002-9939

Journal title

Proceedings of the American Mathematical Society

Volume

125

Issue

3

Pagination

807-813

Publisher

American Mathematical Society (AMS)

Language

en, English

College/Research Centre

Faculty of Science and Information Technology

School

School of Information and Physical Sciences

Rights statement

First published in Proceedings of the American Mathematical Society in Vol. 125, No.3, pp. 807-813, 1997, published by the American Mathematical Society.

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Keywords

Lipschitz function differentiability integrability generalized derivative Clarke subdifferential approximate continuity metric density

Distinct differentiable functions may share the same Clarke subdifferential at all points

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