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
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- Simons S., A convergence theorem with boundary, Pacific J. Math. 40 (1972), 703-708. (1972) Zbl0237.46012MR0312193
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