| Title:
|
On differentiation of metric projections in finite dimensional Banach spaces (English) |
| Author:
|
Zajíček, Luděk |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
33 |
| Issue:
|
3 |
| Year:
|
1983 |
| Pages:
|
325-336 |
| . |
| Category:
|
math |
| . |
| MSC:
|
41A65 |
| MSC:
|
46B20 |
| idZBL:
|
Zbl 0551.41048 |
| idMR:
|
MR718916 |
| DOI:
|
10.21136/CMJ.1983.101883 |
| . |
| Date available:
|
2008-06-09T14:54:47Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/101883 |
| . |
| Reference:
|
[1] E. Asplund: Differentiability of the metric projection in finite-dimensional Euclidean space.Proc. Amer. Math. Soc. 38 (1973), 218-219. Zbl 0269.52002, MR 0310150 |
| Reference:
|
[2] J. Dieudonné: Éléments d'analyse, Tome I: Fondements de l'analyse moderne.Paris 1972. |
| Reference:
|
[3] P. Erdös: On the Hausdorff dimension of some sets in Euclidean space.Bull. Amer. Math. Soc. 52 (1946), 107-109. MR 0015144, 10.1090/S0002-9904-1946-08514-6 |
| Reference:
|
[4] H. Federer: Geometric Measure Theory.Springer-Verlag, New York 1969. Zbl 0176.00801, MR 0257325 |
| Reference:
|
[5] V. Jarník: Differential Calculus II.Prague 1956 (Czech). |
| Reference:
|
[6] P. S. Kenderov: Points of single-valuedness of multivalued monotone mappings in finite dimensional spaces.Serdica 2 (1976), 160-164. Zbl 0346.47044, MR 0477890 |
| Reference:
|
[7] S. V. Konjagin: Approximation properties of arbitrary sets in Banach spaces.Dokl. Akad. Nauk SSSR, 239 (1978), No. 2, 261-264 (Russian). MR 0493113 |
| Reference:
|
[8] J. B. Kruskal: Two convex counterexamples: A discontinuous envelope function and a nondifferentiable nearest-point mapping.Proc. Amer. Math. Soc. 23 (1969), 697-703. Zbl 0184.47401, MR 0259752, 10.1090/S0002-9939-1969-0259752-9 |
| Reference:
|
[9] E. J. Mc Shane: Extension of range of functions.Bull. Amer. Math. Soc. 40 (1934), 837-842. MR 1562984, 10.1090/S0002-9904-1934-05978-0 |
| Reference:
|
[10] F. Mignot: Contrôle dans les inéquations variatonelles Elliptiques.J. Functional Analysis 22 (1976), 130-185. MR 0423155, 10.1016/0022-1236(76)90017-3 |
| Reference:
|
[11] C. J. Neugebauer: A theorem on derivatives.Acta Sci. Math. (Szeged). 23 (1962), 79-81. Zbl 0105.04602, MR 0140624 |
| Reference:
|
[12] R. T. Rockafellar: Convex Analysis.Princeton 1970. Zbl 0193.18401, MR 0274683 |
| Reference:
|
[13] S. Saks: Theory of the Integral.New York 1937. Zbl 0017.30004 |
| Reference:
|
[14] S. Stečkin: Approximation properties of sets in normed linear spaces.Rev. Math. Pures Appl. 8 (1963), 5-18 (Russian). MR 0155168 |
| Reference:
|
[15] Z. Zahorski: Sur l'ensemble des points de nondérivabilité d'une fonction continue.Bull. Soc. Math. France, 74 (1946), 147-178. MR 0022592, 10.24033/bsmf.1381 |
| Reference:
|
[16] L. Zajíček: On the points of multivaluedness of metric projections in separable Banach spaces.Comment. Math. Univ. Carolinae 19 (1978), 513 - 523. MR 0508958 |
| . |
