| Title:
|
Second order differentiability and Lipschitz smooth points of convex functionals (English) |
| Author:
|
Matoušková, Eva |
| Author:
|
Zajíček, Luděk |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
48 |
| Issue:
|
4 |
| Year:
|
1998 |
| Pages:
|
617-640 |
| . |
| Category:
|
math |
| . |
| MSC:
|
26A24 |
| MSC:
|
46G05 |
| MSC:
|
46N10 |
| MSC:
|
49J52 |
| MSC:
|
58C20 |
| idZBL:
|
Zbl 0956.58002 |
| idMR:
|
MR1658221 |
| . |
| Date available:
|
2009-09-24T10:16:40Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127442 |
| . |
| Reference:
|
[A] N. Aronszajn: Differentiability of Lipschitzian mappings between Banach spaces.Studia Math. 57 (1976), 147–190. Zbl 0342.46034, MR 0425608, 10.4064/sm-57-2-147-190 |
| Reference:
|
[BL] Y. Benyamini, J. Lindenstrauss: Geometric Non-linear Functional Analysis.to appear. |
| Reference:
|
[BN] J.M. Borwein, D. Noll: Second order differentiability of convex functions in Banach spaces.Trans. Amer. Math. Soc. 342 (1994), 43–82. MR 1145959, 10.1090/S0002-9947-1994-1145959-4 |
| Reference:
|
[BF] J.M. Borwein, S. Fitzpatrick: Existence of nearest points in Banach spaces.Canad. J. Math. 41 (1989), 702–720. MR 1012624, 10.4153/CJM-1989-032-7 |
| Reference:
|
[C] J.P.R. Christensen: Topology and Borel Structure.North-Holland, Amsterdam, 1974. Zbl 0273.28001, MR 0348724 |
| Reference:
|
[D] R. Dougherty: Examples of non-shy sets.Fundam. Math. 144 (1994), 73–88. Zbl 0842.43006, MR 1271479, 10.4064/fm-144-1-73-88 |
| Reference:
|
[DS] N. Dunford, J.T. Schwarz: Linear Operators I.Interscience Publishers, New York, 1967. |
| Reference:
|
[F] M. Fabian: Lipschitz smooth points of convex functions and isomorphic characterisation of Hilbert spaces.Proc. London Math. Soc. 51 (1985), 113–126. MR 0788852 |
| Reference:
|
[K] K. Kuratowski: Topology I.Academic Press, London, 1968. |
| Reference:
|
[L] S.J. Leese: Measurable selections and the uniformization of Souslin sets.Amer. J. Math. 100 (1978), 19–41. Zbl 0384.28005, MR 0507445, 10.2307/2373874 |
| Reference:
|
[Lt] K. Leichtweiß: Konvexe Mengen.Springer-Verlag, Berlin, 1980. MR 0586235 |
| Reference:
|
[M] P. McMullen: On the inner parallel body of a convex body.Israel J. Math. 19 (1974), 217–219. MR 0367810, 10.1007/BF02757715 |
| Reference:
|
[MM] J. Matoušek, E. Matoušková: A highly non-smooth norm on Hilbert space.(to appear). MR 1715018 |
| Reference:
|
[MS] E. Matoušková, C. Stegall: A characterization of reflexive Banach spaces.Proc. Amer. Math. Soc (to appear). MR 1301517 |
| Reference:
|
[P] R.R. Phelps: Convex Functions, Monotone Operators and Differentiabilitypubl Lecture Notes in Math. 1364, Springer-Verlag, Berlin.1993. MR 1238715 |
| Reference:
|
[R1] R.T. Rockafellar: Convex integral functionals and duality.Contributions to nonlinear functional analysis, E.H. Zarantello (ed.), New York, London, 1971, pp. 215–236. Zbl 0295.49006, MR 0390870 |
| Reference:
|
[R2] R.T. Rockafellar: Integral functionals, normal integrands and measurable selections.Nonlinear operators and the calculus of variations, Lecture Notes in Math. 543, A. Dold and B. Eckmann (eds.), Bruxeles, 1975, pp. 157–207. MR 0512209 |
| Reference:
|
[Rog] C.A. Rogers: Hausdorff Measures.Cambridge Univ. Press, Cambridge, 1970. Zbl 0204.37601, MR 0281862 |
| Reference:
|
[S] S. Solecki: On Haar null sets.Fundam. Math. 149 (1996), 205–210. Zbl 0887.28006, MR 1383206 |
| Reference:
|
[VZ] L. Veselý, L. Zajíček: Delta-convex mappings between Banach spaces and applications.Dissertationes Math. CCLXXXIX, (1989), 48. MR 1016045 |
| . |
