# On Fréchet differentiability of convex functions on Banach spaces

Commentationes Mathematicae Universitatis Carolinae (1995)

- Volume: 36, Issue: 2, page 249-253
- ISSN: 0010-2628

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topTang, Wee-Kee. "On Fréchet differentiability of convex functions on Banach spaces." Commentationes Mathematicae Universitatis Carolinae 36.2 (1995): 249-253. <http://eudml.org/doc/247708>.

@article{Tang1995,

abstract = {Equivalent conditions for the separability of the range of the subdifferential of a given convex Lipschitz function $f$ defined on a separable Banach space are studied. The conditions are in terms of a majorization of $f$ by a $C^1$-smooth function, separability of the boundary for $f$ or an approximation of $f$ by Fréchet smooth convex functions.},

author = {Tang, Wee-Kee},

journal = {Commentationes Mathematicae Universitatis Carolinae},

keywords = {Fréchet differentiability; convex functions; variational principles; Asplund spaces; separability of the range of the subdifferential; convex Lipschitz function; -smooth function; Fréchet smooth convex functions},

language = {eng},

number = {2},

pages = {249-253},

publisher = {Charles University in Prague, Faculty of Mathematics and Physics},

title = {On Fréchet differentiability of convex functions on Banach spaces},

url = {http://eudml.org/doc/247708},

volume = {36},

year = {1995},

}

TY - JOUR

AU - Tang, Wee-Kee

TI - On Fréchet differentiability of convex functions on Banach spaces

JO - Commentationes Mathematicae Universitatis Carolinae

PY - 1995

PB - Charles University in Prague, Faculty of Mathematics and Physics

VL - 36

IS - 2

SP - 249

EP - 253

AB - Equivalent conditions for the separability of the range of the subdifferential of a given convex Lipschitz function $f$ defined on a separable Banach space are studied. The conditions are in terms of a majorization of $f$ by a $C^1$-smooth function, separability of the boundary for $f$ or an approximation of $f$ by Fréchet smooth convex functions.

LA - eng

KW - Fréchet differentiability; convex functions; variational principles; Asplund spaces; separability of the range of the subdifferential; convex Lipschitz function; -smooth function; Fréchet smooth convex functions

UR - http://eudml.org/doc/247708

ER -

## References

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- Phelps R.R., Convex Functions, Monotone Operators and Differentiability, Lect. Notes in Math., Springer-Verlag 1364 (1993) (Second Edition). Zbl0921.46039MR1238715
- Preiss D., Zajíček D., Fréchet differentiation of convex functions in Banach space with separable dual, Proc. Amer. Math. Soc. 91 (1984), 202-204. (1984) MR0740171
- Simons S., A convergence theorem with boundary, Pacific J. Math. 40 (1972), 703-708. (1972) Zbl0237.46012MR0312193

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