Skip to main content

On some problems from the theory of fixed points of multivalued mappings

Part of the Lecture Notes in Mathematics book series (LNM,volume 1453)

Keywords

  • Fixed Point Theorem
  • Multivalued Mapping
  • Topological Characteristic
  • Lefschetz Number
  • Leray Spectral Sequence

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   34.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   46.00
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Kakytani S., A generalization of Brouwer's fixed point theorem, Duke Math. J., 1941, 8, p. 457–459.

    CrossRef  MathSciNet  Google Scholar 

  2. Eilenberg S., Montgomery D. Fixed point theorems for multivalued transformations, Amer. J. Math., 1946, 68, p. 214–222.

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. Gel'man B.D. The topological characteristic of multivalued mappings and fixed point theorems. Doklady AN SSSR, 1975, 221 (3), p. 524–527 (in Russian; see English translation in Soviet Math. Doklady, 1975, vol.16, No 2).

    MathSciNet  MATH  Google Scholar 

  4. Gel'man B.D. Topological characteristic of multivalued mappings in Banach space. Trudy Mt. Fak. Voronezh Univ., 1975, 16, p. 17–23 (in Russian).

    MathSciNet  Google Scholar 

  5. Borisovich Yu.G., Gel'man B.D., Myshkis A.D., Obukhovskii V.V. Topological methods in the theory of fixed points of set-valued mappings. Uspekhi Mat. Nauk, 1980, 35 (1), p. 59–126 (in Russian; see English translation in Russian Math. Surveys).

    MathSciNet  Google Scholar 

  6. Borisovich Yu.G., Gel'man B.D., Myshkis A.D., Obukhovskii V.V. Multivalued analysis and operator imbeddings. Itogi Nauki i Tekhniki, VINITI, Sovr. Probl. Mat., 1986, 29, p. 151–211 (in Russian).

    MathSciNet  Google Scholar 

  7. Benkafadar N., Gel'man B.D. On homotopical properties of subset spaces. In: Topological and geometrical methods in mathematical physics, Voronezh, 1983, p. 111–115 (in Russian).

    Google Scholar 

  8. Spanier E.H. Algebraic topology. McGraw-Hill, New York, 1966.

    MATH  Google Scholar 

  9. Sklyarenko V.G. On some applications of the bundle theory in general topology, Uspekhi Mat. Nauk, 1964, 19 (6), p. 47–70 (in Russian).

    MathSciNet  MATH  Google Scholar 

  10. Myshkis A.D. Generalizations of the fixed point theorem of a dynamic system in closed trajectory. Mat. Sb., 1954, 34 (3), p. 525–540 (in Russian).

    MathSciNet  MATH  Google Scholar 

  11. Borisovich Yu.G., Gliklikh Yu.E. On Lefschetz number for one class of multivalued mappings. In: 7th summer math. school, Kiev, 1970, p. 283–294 (in Russian).

    Google Scholar 

  12. Gel'man B.D. A generalization of the Kakutani's fixed point theorem to many-valued mappings. Doklady Akad. Nauk SSSR, 1973, 209 (1), 22–24 (in Russian; see English translation in Soviet Math. Doklady, 1973, vol. 14, No 2).

    MathSciNet  MATH  Google Scholar 

  13. Godement R. Topologie algébrique et theorie des faisceaux. Hermann, Paris, 1958.

    MATH  Google Scholar 

  14. Gel'man B.D. On certain classes of selections of many-valued mappings. In: Applications of topology to contemporary analysis, Voronezh, 1985, p. 42–62 (in Russian; see English translation in Lect. Notes Math., 1986, vol. 1214).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1990 Springer-Verlag

About this chapter

Cite this chapter

Gel'man, B.D. (1990). On some problems from the theory of fixed points of multivalued mappings. In: Borisovich, Y.G., Gliklikh, Y.E., Vershik, A.M. (eds) Global Analysis - Studies and Applications IV. Lecture Notes in Mathematics, vol 1453. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0085958

Download citation

  • DOI: https://doi.org/10.1007/BFb0085958

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-53407-5

  • Online ISBN: 978-3-540-46861-5

  • eBook Packages: Springer Book Archive