Smallness of sets of nondifferentiability of convex functions in non-separable Banach spaces

Luděk Zajíček

Czechoslovak Mathematical Journal (1991)

  • Volume: 41, Issue: 2, page 288-296
  • ISSN: 0011-4642

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Zajíček, Luděk. "Smallness of sets of nondifferentiability of convex functions in non-separable Banach spaces." Czechoslovak Mathematical Journal 41.2 (1991): 288-296. <http://eudml.org/doc/13927>.

@article{Zajíček1991,
author = {Zajíček, Luděk},
journal = {Czechoslovak Mathematical Journal},
keywords = {-porous set; cone-small sets; maximal monotone operator; Asplund space},
language = {eng},
number = {2},
pages = {288-296},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Smallness of sets of nondifferentiability of convex functions in non-separable Banach spaces},
url = {http://eudml.org/doc/13927},
volume = {41},
year = {1991},
}

TY - JOUR
AU - Zajíček, Luděk
TI - Smallness of sets of nondifferentiability of convex functions in non-separable Banach spaces
JO - Czechoslovak Mathematical Journal
PY - 1991
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 41
IS - 2
SP - 288
EP - 296
LA - eng
KW - -porous set; cone-small sets; maximal monotone operator; Asplund space
UR - http://eudml.org/doc/13927
ER -

References

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  1. N. Aronszajn, Differentiability of Lipschitzian mappings between Banach spaces, Studia Math. 57 (1976), 147-190. (1976) Zbl0342.46034MR0425608
  2. P. S. Kenderov, The set-valued monotone mappings are almost everywhere single-valued, C. R. Acad. Bulgare Sci. 27 (1974), 1173-1175. (1974) Zbl0339.47024MR0358447
  3. P. S. Kenderov, Monotone operators in Asplund spaces, C. R. Acad. Bulgare Sci. 30 (1977), 963-964. (1977) Zbl0377.47036MR0463981
  4. S. V. Konjagin, On the points of the existence and nonunicity of elements of the best approximation, (in Russian), in Teorija funkcij i ee prilozhenija, P. L. Uljanov ed., Izdatelstvo Moskovskovo Universiteta, pp. 38-43, Moscow (1986). (1986) 
  5. K. Kuratowski, Topology, Vol. I, (transl.), Academic Press, New York (1966). (1966) Zbl0158.40901MR0217751
  6. R. R. Phelps, Convex functions, monotone operators and differentiability, Lect. Notes in Math., Nr. 1364, Springer-Verlag, (1989). (1989) Zbl0658.46035MR0984602
  7. D. Preiss, L. Zajíček, Fréchet differentiation of convex functions in a Banach space with a separable dual, Proc. Amer. Math. Soc. 91 (1984), 202-204. (1984) MR0740171
  8. D. Preiss, L. Zajíček, Stronger estimates of smallness of sets of Fréchet nondifferentiability of convex functions, Proc. 11th Winter School, Suppl. Rend. Circ. Mat. Palermo, Ser. II, No. 3 (1984), 219-223. (1984) MR0744387
  9. L. Zajíček, On the differentiation of convex functions in finite and infinite dimensional spaces, Czechoslovak Math. J. 29 (104) (1979), 340-348. (1979) MR0536060
  10. L. Zajíček, Differentiability of the distance function and points of multi-valuedness of the metric projection in Banach space, Czechoslovak Math. J. 33 (108), (1983), 292-308. (1983) MR0699027
  11. L. Zajíček, Porosity and σ -porosity, Real Analysis Exchange 13 (1987-88), 314 - 350. (1987) MR0943561
  12. 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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