On differentiation of metric projections in finite dimensional Banach spaces

Luděk Zajíček

Czechoslovak Mathematical Journal (1983)

  • Volume: 33, Issue: 3, page 325-336
  • ISSN: 0011-4642

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Zajíček, Luděk. "On differentiation of metric projections in finite dimensional Banach spaces." Czechoslovak Mathematical Journal 33.3 (1983): 325-336. <http://eudml.org/doc/13387>.

@article{Zajíček1983,
author = {Zajíček, Luděk},
journal = {Czechoslovak Mathematical Journal},
keywords = {finite-dimensional Banach space; Frechet derivative; metric projection},
language = {eng},
number = {3},
pages = {325-336},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On differentiation of metric projections in finite dimensional Banach spaces},
url = {http://eudml.org/doc/13387},
volume = {33},
year = {1983},
}

TY - JOUR
AU - Zajíček, Luděk
TI - On differentiation of metric projections in finite dimensional Banach spaces
JO - Czechoslovak Mathematical Journal
PY - 1983
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 33
IS - 3
SP - 325
EP - 336
LA - eng
KW - finite-dimensional Banach space; Frechet derivative; metric projection
UR - http://eudml.org/doc/13387
ER -

References

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  1. E. Asplund, Differentiability of the metric projection in finite-dimensional Euclidean space, Proc. Amer. Math. Soc. 38 (1973), 218-219. (1973) Zbl0269.52002MR0310150
  2. J. Dieudonné, Éléments d'analyse, Tome I: Fondements de l'analyse moderne, Paris 1972. (1972) 
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  4. H. Federer, Geometric Measure Theory, Springer-Verlag, New York 1969. (1969) Zbl0176.00801MR0257325
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  6. P. S. Kenderov, Points of single-valuedness of multivalued monotone mappings in finite dimensional spaces, Serdica 2 (1976), 160-164. (1976) Zbl0346.47044MR0477890
  7. S. V. Konjagin, Approximation properties of arbitrary sets in Banach spaces, Dokl. Akad. Nauk SSSR, 239 (1978), No. 2, 261-264 (Russian). (1978) MR0493113
  8. J. B. Kruskal, 10.1090/S0002-9939-1969-0259752-9, Proc. Amer. Math. Soc. 23 (1969), 697-703. (1969) Zbl0184.47401MR0259752DOI10.1090/S0002-9939-1969-0259752-9
  9. E. J. Mc Shane, 10.1090/S0002-9904-1934-05978-0, Bull. Amer. Math. Soc. 40 (1934), 837-842. (1934) MR1562984DOI10.1090/S0002-9904-1934-05978-0
  10. F. Mignot, 10.1016/0022-1236(76)90017-3, J. Functional Analysis 22 (1976), 130-185. (1976) MR0423155DOI10.1016/0022-1236(76)90017-3
  11. C. J. Neugebauer, A theorem on derivatives, Acta Sci. Math. (Szeged). 23 (1962), 79-81. (1962) Zbl0105.04602MR0140624
  12. R. T. Rockafellar, Convex Analysis, Princeton 1970. (1970) Zbl0193.18401MR0274683
  13. S. Saks, Theory of the Integral, New York 1937. (1937) Zbl0017.30004
  14. S. Stečkin, Approximation properties of sets in normed linear spaces, Rev. Math. Pures Appl. 8 (1963), 5-18 (Russian). (1963) MR0155168
  15. Z. Zahorski, 10.24033/bsmf.1381, Bull. Soc. Math. France, 74 (1946), 147-178. (1946) MR0022592DOI10.24033/bsmf.1381
  16. L. Zajíček, On the points of multivaluedness of metric projections in separable Banach spaces, Comment. Math. Univ. Carolinae 19 (1978), 513 - 523. (1978) MR0508958

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