| Title:
|
On Fréchet differentiability of convex functions on Banach spaces (English) |
| Author:
|
Tang, Wee-Kee |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
36 |
| Issue:
|
2 |
| Year:
|
1995 |
| Pages:
|
249-253 |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
Fréchet differentiability |
| Keyword:
|
convex functions |
| Keyword:
|
variational principles |
| Keyword:
|
Asplund spaces |
| MSC:
|
46B03 |
| MSC:
|
46G05 |
| MSC:
|
49J50 |
| MSC:
|
58C20 |
| idZBL:
|
Zbl 0831.46045 |
| idMR:
|
MR1357526 |
| . |
| Date available:
|
2009-01-08T18:17:39Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118753 |
| . |
| Reference:
|
[As-R] Asplund E., Rockafellar R.T.: Gradients of convex functions.Trans. Amer. Math. Soc. 139 (1968), 443-467. MR 0240621 |
| Reference:
|
[DGZ] Deville R., Godefroy G., Zizler V.: Renormings and Smoothness in Banach Spaces.Pitman Monograph and Survey in Pure and Applied Mathematics 64. |
| Reference:
|
[F] Fabian M.: On projectional resolution of identity on the duals of certain Banach spaces.Bull. Austral. Math Soc. 35 (1987), 363-371. MR 0888895 |
| Reference:
|
[G] Godefroy G.: Some applications of Simons' inequality.Seminar of Functional Analysis II, Univ. of Murcia, to appear. MR 1767034 |
| Reference:
|
[MPVZ] McLaughlin D., Poliquin R.A., Vanderwerff J.D., Zizler V.E.: Second order Gateaux differentiable bump functions and approximations in Banach spaces.Can. J. Math 45:3 (1993), 612-625. Zbl 0796.46005, MR 1222519 |
| Reference:
|
[Ph] Phelps R.R.: Convex Functions, Monotone Operators and Differentiability.Lect. Notes in Math., Springer-Verlag 1364 (1993) (Second Edition). Zbl 0921.46039, MR 1238715 |
| Reference:
|
[Pr-Z] Preiss D., Zajíček D.: Fréchet differentiation of convex functions in Banach space with separable dual.Proc. Amer. Math. Soc. 91 (1984), 202-204. MR 0740171 |
| Reference:
|
[S] Simons S.: A convergence theorem with boundary.Pacific J. Math. 40 (1972), 703-708. Zbl 0237.46012, MR 0312193 |
| . |
