A note on the differentiability of convex functions

Authors:
Cong Xin Wu and Li Xin Cheng

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

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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 , then, for each Gateaux differentiability point *x* of *f*, there is a closed convex set with the nonsupport points set and with such that (the restriction of *f* on *C*) is Fréchet differentiable at *x*.

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DOI:
https://doi.org/10.1090/S0002-9939-1994-1207535-X

Article copyright:
© Copyright 1994
American Mathematical Society