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Distinct differentiable functions may share the same Clarke subdifferential at all points |
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| Authors: | J. M. Borwein Xianfu Wang |
| Affiliation: | Department of Mathematics and Statistics, Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6 ; Department of Mathematics and Statistics, Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6 |
| Abstract: | 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. |
| Keywords: | Lipschitz function differentiability integrability generalized derivative Clarke subdifferential approximate continuity metric density |
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