| Title:
|
Differentiability of the distance function and points of multi-valuedness of the metric projection in Banach space (English) |
| Author:
|
Zajíček, Luděk |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
33 |
| Issue:
|
2 |
| Year:
|
1983 |
| Pages:
|
292-308 |
| . |
| Category:
|
math |
| . |
| MSC:
|
41A50 |
| MSC:
|
46B20 |
| idZBL:
|
Zbl 0527.41028 |
| idMR:
|
MR699027 |
| DOI:
|
10.21136/CMJ.1983.101878 |
| . |
| Date available:
|
2008-06-09T14:54:26Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/101878 |
| . |
| Reference:
|
[1] T. Abatzoglou: Finite-dimensional Banach spaces with a.e. differentiable metric projection.Proc. Amer. Math. Soc. 78 (1980), 492-496. Zbl 0475.41035, MR 0556619, 10.1090/S0002-9939-1980-0556619-8 |
| Reference:
|
[2] A. D. Aleksandrov: Existence almost everywhere of the second differential of a convex function and some properties of convex surfaces connected with it.(Russian), Učenye Zapiski Leningrad. Gos. Univ. Math. Ser. 6 (1939), 3 - 35. |
| Reference:
|
[3] 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:
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[4] E. Asplund: Differentiability of the metric projection in finite-dimensional Euclidean spaces.Proc. Amer. Math. Soc. 38 (1973), 218-219. MR 0310150 |
| Reference:
|
[5] H. Blumberg: Exceptional sets.Fund. Math. 32 (1939), 3 - 32. Zbl 0021.11206, 10.4064/fm-32-1-3-32 |
| Reference:
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[6] G. Bouligand: Sur la distance d'un point variable a un ensemble fixe.C. R. Acad. Sci. Paris 206 (1938), 552-554. Zbl 0018.17301 |
| Reference:
|
[7] E. P. Dolženko: Boundary properties of arbitrary functions.(Russian), Izv. Akad. Nauk SSSR, Ser. Mat. 31 (1967), 3-14. MR 0217297 |
| Reference:
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[8] 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:
|
[9] S. Fitzpatrick: Metric projection and the differentiability of distance functions.Bull. Austral. Math. Soc. 22 (1980), 291-312. MR 0598702, 10.1017/S0004972700006596 |
| Reference:
|
[10] S. Golab: Sur la fonction representant la distance d'un point variable a un ensemble fixe.С. R. Acad. Sci. Paris 206 (1938), 406-408. Zbl 0018.17205 |
| Reference:
|
[11] P. Hartman: On Functions representable as a Difference of Convex Functions.Pacific J. Math. 9 (1959), 707-713. Zbl 0093.06401, MR 0110773, 10.2140/pjm.1959.9.707 |
| Reference:
|
[12] S. V. Konjagin: Approximation properties of arbitrary sets in Banach spaces.Dokl. Akad. Nauk SSSR 239 (1978), No. 2, 261-264, Soviet. Math. Dokl. 19 (1978), No. 2, 309-312. MR 0493113 |
| Reference:
|
[13] S. V. Konjagin: On approximation properties of closed sets in Banach spaces and the characterization of strongly convex spaces.(Russian), Dokl. Akad. Nauk SSSR 251 (1980), No. 2, 276-280, Soviet. Math. Dokl. 21 (1980), No. 2, 418-422. MR 0565493 |
| Reference:
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[14] 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:
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[15] F. Mignot: Controle dans les inéqualitions variationelles elliptiques.J. Functional Analysis 22 (1976), 130-185. MR 0423155, 10.1016/0022-1236(76)90017-3 |
| Reference:
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[16] M. R. de Mises: La base géométrique du théoreme de M. Mandelbrojt sur les points singuliers d'une fonction analytique.C. R. Acad. Sci. Paris 205 (1937), 1353 - 1355. Zbl 0017.42601 |
| Reference:
|
[17] R. R. Phelps: Gaussian null sets and differentiability of Lipschitz maps on Banach spaces.Pacific J. Math. 18 (1978), 523-531. MR 0510938, 10.2140/pjm.1978.77.523 |
| Reference:
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[18] Ju. G. Resetnjak: On a generalization of convex surfaces.(Russian), Mat. Sbornik 40 (82) (1956), 381-398. MR 0083757 |
| Reference:
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[19] A. W. Roberts, D. E. Varberg: Convex functions.New York, 1973. Zbl 0271.26009, MR 0442824 |
| Reference:
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[20] S. Saks: Theory of the Integral.New York, 1937. Zbl 0017.30004 |
| Reference:
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[21] W. H. Young: La symétrie de structure des fonctions de variables réeles.Bull. Sci. Math. 52 (1928), 265-280. |
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[22] L. Zajíček: On cluster sets of arbitrary functions.Fund. Math, 83 (1974), 197-217. MR 0338294, 10.4064/fm-83-3-197-217 |
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[23] L. Zajíček: Sets of $\sigma$-porosity and sets of $\sigma$-porosity.(q). Čas. pěst. mat. 101 (1976), 350-359. MR 0457731 |
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[24] L. Zajíček: On the points of multiplicity of monotone operators.Comment. Math. Univ. Carolinae 19 (1978), 179-189. MR 0493541 |
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[25] L. Zajíček: On the points of multivaluedness of metric projections in separable Banach spaces.Comment. Math. Univ. Carolinae 19 (1978), 513 - 523. MR 0508958 |
| Reference:
|
[26] L. Zajíček: On the differentiation of convex functions in finite and infinite dimensional spaces.Czechoslovak Math. J. 29 (104) (1979), 340-348. MR 0536060 |
| Reference:
|
[27] L. Zajíček: On metric projections and distance functions in Banach spaces.Abstracta of Eighth winter school on abstract analysis (1980), 207-208, Prague 1980. |
| . |
