## A note on the differentiability of convex functions

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- by Cong Xin Wu and Li Xin Cheng PDF
- Proc. Amer. Math. Soc.
**121**(1994), 1057-1062 Request permission

## Abstract:

Every real-valued convex and locally Lipschitzian function*f*defined on a nonempty closed convex set

*D*of a Banach space

*E*is the local restriction of a convex Lipschitzian function defined on

*E*. Moreover, if

*E*is separable and $\operatorname {int} D \ne \emptyset$, then, for each Gateaux differentiability point

*x*$( \in \operatorname {int} D)$ of

*f*, there is a closed convex set $C \subset \operatorname {int} D$ with the nonsupport points set $N(C) \ne \emptyset$ and with $x \in N(C)$ such that ${f_C}$ (the restriction of

*f*on

*C*) is FrĂ©chet differentiable at

*x*.

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## Additional Information

- © Copyright 1994 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**121**(1994), 1057-1062 - MSC: Primary 46G05; Secondary 49J50
- DOI: https://doi.org/10.1090/S0002-9939-1994-1207535-X
- MathSciNet review: 1207535