Siberian Mathematical Journal

, Volume 35, Issue 3, pp 479–494 | Cite as

Continuous selections for a family of nonconvex-valued mappings with noncompact domain

  • V. V. Goncharov
  • A. A. Tolstonogov


Continuous Selection Noncompact Domain 
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  1. 1.
    V. V. Goncharov and A. A. Tolstonogov, “Common continuous selections of multivalued mappings with nonconvex values and their applications,” Mat. Sb.,182, No. 7, 946–969 (1991).Google Scholar
  2. 2.
    A. Fryszkowski, “Continuous selections for a class of nonconvex multivalued maps,” Studia Math.,76, No. 2, 163–174 (1983).Google Scholar
  3. 3.
    A. Bressan and G. Colombo, “Extensions and selections of maps with decomposable values,” Studia Math.,90, No. 1, 69–86 (1988).Google Scholar
  4. 4.
    A. Ornelas, Approximation of Relaxed Solutions for Lower Semicontinuous Differential Inclusions [Preprint, International School for Advanced Studies; No. 102/86/M], Italy, Trieste (1986).Google Scholar
  5. 5.
    A. I. Bulgakov, “On the question of existence of continuous branches for multivalued mappings with nonconvex images in spaces of summable functions,” Mat. Sb.,136, No. 2, 292–300 (1988).Google Scholar
  6. 6.
    A. A. Tolstonogov, “Extremal selectors of multivalued mappings and the ‘bang-bang’ principle for evolution inclusions,” Dokl. Akad. Nauk SSSR,317, No. 3, 589–593 (1991).Google Scholar
  7. 7.
    P. R. Halmos, Measure Theory [Russian translation], Izdat. Inostr. Lit., Moscow (1953).Google Scholar
  8. 8.
    J. L. Kelley, General Topology [Russian translation], Nauka, Moscow (1981).Google Scholar
  9. 9.
    R. E. Edwards, Functional Analysis. Theory and Applications [Russian translation], Mir, Moscow (1969).Google Scholar
  10. 10.
    K. Kuratowski, Topology. Vol. I [Russian translation], Mir, Moscow (1966).Google Scholar
  11. 11.
    A. A. Tolstonogov, “On certain properties of spaces of sublinear functionals,” Sibirsk. Mat. Zh.,18, No. 2, 429–443 (1977).Google Scholar
  12. 12.
    A. A. Tolstonogov and V. V. Goncharov, “On sublinear functionals defined on the space of Bochner integrable functions,” Sibirsk. Mat. Zh.,35, No. 1, 194–206 (1994).Google Scholar
  13. 13.
    E. Michael, “Continuous selections. I,” Ann. of Math. (2),63, 361–382 (1956).Google Scholar
  14. 14.
    F. S. De Blasi and G. Pianigiani, “Remarks on Hausdorff continuous multifunctions and selections,” Comment. Math. Univ. Carolin.,24, No. 3, 553–561 (1983).Google Scholar
  15. 15.
    F. Hiai and H. Umegaki, “Integrals, conditional expectations, and martingales of multivalued functions,” J. Multivariate Anal.,7, No. 1, 149–182 (1977).CrossRefGoogle Scholar
  16. 16.
    Van Chu'o'ng Phan, “A density theorem with an application in relaxation of nonconvex-valued differential equations,” Sém. Anal. Convexe, Univ. Sci. Tech. Languedoc,15, No. 2, 2.1–2.22 (1985).Google Scholar

Copyright information

© Plenum Publishing Corporation 1994

Authors and Affiliations

  • V. V. Goncharov
    • 1
  • A. A. Tolstonogov
    • 1
  1. 1.Irkutsk

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