Skip to main content
Log in

Differentiable and Lipschitzian mappings of Banach spaces

  • Published:
Mathematical notes of the Academy of Sciences of the USSR Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Literature cited

  1. D. Preiss, “Gâteaux-differentiable functions are somewhere Fréchet differentiable,” Rend. Circ. Mat. Palermo (2),33, No. 1, 122–133 (1984).

    Google Scholar 

  2. D. Preiss, “Gâteaux-differentiable Lipschitz functions need not be Fréchet differentiable on a residual set,” Supplemento Rend. Circ. Mat. Palermo (2), No. 2, 217–222 (1982).

    Google Scholar 

  3. V. I. Averbukh and O. G. Smolyanov, “Different definitions of the derivative in linear topological spaces,” Usp. Mat. Nauk,23, No. 4, 67–116 (1968).

    Google Scholar 

  4. V. I. Averbukh, O. G. Smolyanov, and S. V. Fomin, “Generalized functions and differential equations in linear spaces,” Trudy MMO,24, 132–174 (1971).

    Google Scholar 

  5. J. L. Kelley, General Topology, Van Nostrand, Princeton, N.J. (1955).

    Google Scholar 

  6. C. Kuratowski, Topologie, I, Warsaw (1948).

  7. G. Lebourg, “Generic differentiability of Lipschitzian functions,” Trans. Am. Math. Soc.,256, 125–144 (1979).

    Google Scholar 

  8. M. Sova, “Differentiability conditions in linear topologial spaces,” Chekhoslov. Mat. Zh.,16, No. 3, 339–362 (1966).

    Google Scholar 

  9. N. Aronszajn, “Differentiability of Lipschitzian mappings between Banach spaces,” Stud. Math.,57, No. 2, 147–190 (1976).

    Google Scholar 

  10. J. Diestel, Geometry of Banach Spaces — Selected Topics, Springer, Berlin (1975).

    Google Scholar 

  11. A. M. Bruckner, Differentiation of Real Functions, Springer, Heidelberg (1978).

    Google Scholar 

  12. B. J. Pettis, “On the Radon-Nikodym theorem,” Lect. Notes Mat.,644, 340–355 (1978).

    Google Scholar 

  13. R. R. Phelps, “Gaussian null sets and differentiability of Lipschitz maps on Banach spaces,” Pac. J. Math.,77, No. 3, 523–531 (1978).

    Google Scholar 

  14. V. I. Bogachev, “Negligible sets and differentiable measures in Banach spaces,” Vestn. Mosk. Gos. Univ. Ser. 1. Mat., Mekh., No. 3, 47–52 (1982).

    Google Scholar 

  15. V. Goodman, “Quasidifferentiable functions on Banach spaces,” Proc. Am. Math. Soc.,30, No. 2, 367–370 (1971).

    Google Scholar 

  16. L. Gross, “Potential theory on Hilbert space,” J. Func. Anal.,1, 123–181 (1967).

    Google Scholar 

  17. R. Bonic and J. Frampton, “Differentiable functions on certain Banach spaces,” Bull. Am. Math. Soc.,71, No. 2, 393–395 (1965).

    Google Scholar 

  18. A. S. Nemirovskii and S. M. Semenov, “On polynomial approximation of functions on Hilbert space,” Mat. Sb.,92, No. 2, 257–281 (1973).

    Google Scholar 

  19. J. Kurzweil, “On approximation in real Banach spaces,” Stud. Math.,14, No. 2, 214–231 (1954).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Translated from Matematicheskie Zametki, Vol. 44, No. 5, pp. 567–583, November, 1988.

The authors would like to thank O. G. Smolyanov for his attention to the paper and S. V. Konyagin for his useful comments.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bogachev, V.I., Shkarin, S.A. Differentiable and Lipschitzian mappings of Banach spaces. Mathematical Notes of the Academy of Sciences of the USSR 44, 790–798 (1988). https://doi.org/10.1007/BF01158417

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01158417

Keywords

Navigation