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Siberian Mathematical Journal

, Volume 33, Issue 5, pp 905–913 | Cite as

On continuity points of Gateaux differentiable mappings

  • S. A. Shkarin
Article

Keywords

Differentiable Mapping Continuity Point Gateau Differentiable Mapping 
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References

  1. 1.
    D. Presis, “Gateaux differentiable functions are somewhere Fréchet differentiable,” Rend. Circ. Mat. Palermo,33, No. 1, 122–133 (1984).Google Scholar
  2. 2.
    V. I. Bogachev and S. A. Shkarin, “On differentiable and Lipschitz continuous mappings on Banach spaces,” Mat. Zametki,44, No. 5, 567–583 (1988).Google Scholar
  3. 3.
    D. Presis, “Differentiability of Lipschitz functions on Banach spaces,” J. Funct. Anal.,91, No. 2, 312–345 (1990).Google Scholar
  4. 4.
    J. Oxtoby, Measure and Category [Russian translation], Mir, Moscow (1974).Google Scholar
  5. 5.
    A. P. Robertson and W. Robertson, Topological Vector Spaces [Russian translation], Mir, Moscow (1967).Google Scholar
  6. 6.
    V. I. Averbukh and O. G. Smolyanov, “Various definitions of a derivative in linear topological spaces,” Uspekhi Mat. Nauk,23, No. 4, 67–116 (1968).Google Scholar
  7. 7.
    D. Presis, “Gateaux differentiable Lipschitz functions need not be Fréchet differentiable on a resudual set,” Rend. Circ. Mat. Palermo (2) Suppl., No. 2, 217–222 (1982).Google Scholar
  8. 8.
    E. Stein, Singular Integrals and Differentiability Properties of Functions [Russian translation], Mir, Moscow (1973).Google Scholar
  9. 9.
    J. Diestel, Geometry of Banach Spaces [in Russian], Vyssh. Shk., Kiev (1980).Google Scholar
  10. 10.
    J. Bonet and C. P. Perez, “Barrelled locally convex spaces,” Ann. of Math. Stud.,131 (1987).Google Scholar

Copyright information

© Plenum Publishing Corporation 1992

Authors and Affiliations

  • S. A. Shkarin

There are no affiliations available

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