@article{10_21136_CMJ_1983_101878,
author = {Zaj{\'\i}\v{c}ek, Lud\v{e}k},
title = {Differentiability of the distance function and points of multi-valuedness of the metric projection in {Banach} space},
journal = {Czechoslovak Mathematical Journal},
pages = {292--308},
year = {1983},
volume = {33},
number = {2},
doi = {10.21136/CMJ.1983.101878},
mrnumber = {699027},
zbl = {0527.41028},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.21136/CMJ.1983.101878/}
}
TY - JOUR AU - Zajíček, Luděk TI - Differentiability of the distance function and points of multi-valuedness of the metric projection in Banach space JO - Czechoslovak Mathematical Journal PY - 1983 SP - 292 EP - 308 VL - 33 IS - 2 UR - http://geodesic.mathdoc.fr/articles/10.21136/CMJ.1983.101878/ DO - 10.21136/CMJ.1983.101878 LA - en ID - 10_21136_CMJ_1983_101878 ER -
%0 Journal Article %A Zajíček, Luděk %T Differentiability of the distance function and points of multi-valuedness of the metric projection in Banach space %J Czechoslovak Mathematical Journal %D 1983 %P 292-308 %V 33 %N 2 %U http://geodesic.mathdoc.fr/articles/10.21136/CMJ.1983.101878/ %R 10.21136/CMJ.1983.101878 %G en %F 10_21136_CMJ_1983_101878
Zajíček, Luděk. Differentiability of the distance function and points of multi-valuedness of the metric projection in Banach space. Czechoslovak Mathematical Journal, Tome 33 (1983) no. 2, pp. 292-308. doi: 10.21136/CMJ.1983.101878
[1] T. Abatzoglou: Finite-dimensional Banach spaces with a.e. differentiable metric projection. Proc. Amer. Math. Soc. 78 (1980), 492-496. | DOI | MR | Zbl
[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.
[3] N. Aronszajn: Differentiability of Lipschitzian mappings between Banach spaces. Studia Math. 57 (1976), 147-190. | DOI | MR | Zbl
[4] E. Asplund: Differentiability of the metric projection in finite-dimensional Euclidean spaces. Proc. Amer. Math. Soc. 38 (1973), 218-219. | MR
[5] H. Blumberg: Exceptional sets. Fund. Math. 32 (1939), 3 - 32. | DOI | Zbl
[6] G. Bouligand: Sur la distance d'un point variable a un ensemble fixe. C. R. Acad. Sci. Paris 206 (1938), 552-554. | Zbl
[7] E. P. Dolženko: Boundary properties of arbitrary functions. (Russian), Izv. Akad. Nauk SSSR, Ser. Mat. 31 (1967), 3-14. | MR
[8] P. Erdös: On the Hausdorff dimension of some sets in Euclidean space. Bull. Amer. Math. Soc. 52 (1946), 107-109. | DOI | MR
[9] S. Fitzpatrick: Metric projection and the differentiability of distance functions. Bull. Austral. Math. Soc. 22 (1980), 291-312. | DOI | MR
[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
[11] P. Hartman: On Functions representable as a Difference of Convex Functions. Pacific J. Math. 9 (1959), 707-713. | DOI | MR | Zbl
[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
[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
[14] E. J. Mc Shane: Extension of range of functions. Bull. Amer. Math. Soc. 40 (1934), 837-842. | DOI | MR
[15] F. Mignot: Controle dans les inéqualitions variationelles elliptiques. J. Functional Analysis 22 (1976), 130-185. | DOI | MR
[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
[17] R. R. Phelps: Gaussian null sets and differentiability of Lipschitz maps on Banach spaces. Pacific J. Math. 18 (1978), 523-531. | DOI | MR
[18] Ju. G. Resetnjak: On a generalization of convex surfaces. (Russian), Mat. Sbornik 40 (82) (1956), 381-398. | MR
[19] A. W. Roberts, D. E. Varberg: Convex functions. New York, 1973. | MR | Zbl
[20] S. Saks: Theory of the Integral. New York, 1937. | Zbl
[21] W. H. Young: La symétrie de structure des fonctions de variables réeles. Bull. Sci. Math. 52 (1928), 265-280.
[22] L. Zajíček: On cluster sets of arbitrary functions. Fund. Math, 83 (1974), 197-217. | DOI | MR
[23] L. Zajíček: Sets of $\sigma$-porosity and sets of $\sigma$-porosity. (q). Čas. pěst. mat. 101 (1976), 350-359. | MR
[24] L. Zajíček: On the points of multiplicity of monotone operators. Comment. Math. Univ. Carolinae 19 (1978), 179-189. | MR
[25] L. Zajíček: On the points of multivaluedness of metric projections in separable Banach spaces. Comment. Math. Univ. Carolinae 19 (1978), 513 - 523. | MR
[26] L. Zajíček: On the differentiation of convex functions in finite and infinite dimensional spaces. Czechoslovak Math. J. 29 (104) (1979), 340-348. | MR
[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.
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