Download PDF - On the Nielsen fixed point theory for multivalued mappingsAll rights reserved. Copyright exceptions and limitations apply

ArticleOriginal scientific text

Title

On the Nielsen fixed point theory for multivalued mappings

Authors 1

Affiliations

  1. Institute of Mathematics, University of Gdańsk, Wita Stwosza 57, 80-952 Gdańsk, Poland

Abstract

We present J. Jezierski's approach to the Nielsen fixed point theory for a broad class of multivalued mappings [Je1]. We also describe some generalizations and different techniques existing in the literature.

Bibliography

  1. [An] J. Andres, Multiple bounded solutions of differential inclusions: The Nielsen theory approach, Preprint (1997).
  2. [AC] J. P. Aubin and A. Cellina, Differential Inclusions, Springer-Verlag, 1984.
  3. [Bro] R. F. Brown, The Lefschetz Fixed Point Theorem, Scott, Foresman & Co., Glenview Ill., 1971.
  4. [Do] A. Dold, Lectures on Algebraic Topology, Springer-Verlag, 1972.
  5. [Dz1] Z. Dzedzej, Fixed point index theory for a class of non-acyclic multivalued maps, Dissertationes Math. 253 (1985).
  6. [Dz2] Z. Dzedzej, On Nielsen and Reidemeister relations for set-valued symmetric product maps, CRM Barcelona 76 (1989), 1-8.
  7. [Gor] L. Górniewicz, Topological approach to differential inclusions, in: Topol. Methods in Diff. Equations and Inclusions, A. Granas and M. Frigon (eds.), NATO ASI 472, 129-190.
  8. [GGK] L. Górniewicz, A. Granas and W. Kryszewski, On the homotopy method in the fixed point index theory for multivalued mappings of compact ANR's, J. Math. Anal. Appl. 161 (1991), 457-473.
  9. [Je1] J. Jezierski, The Nielsen relation for multivalued maps, Serdica 13 (1987), 174-181.
  10. [Je2] J. Jezierski, An example of finitely-valued fixed point free map, Zesz. Nauk. IM UG 6 (1987), 87-93.
  11. [Jia] B. Jiang, Lectures on Nielsen Fixed Point Theory, Contemp. Math. 14, AMS, Providence, R.I., 1983.
  12. [KrM] W. Kryszewski and D. Miklaszewski, The Nielsen number of set-valued maps. An approximation approach, Serdica 15 (1989), 336-344.
  13. [Mas] S. Masih, On the fixed point index and Nielsen fixed point theorem for symmetric product mappings, Fund. Math. 102 (1979), 143-158.
  14. [Mik] D. Miklaszewski, A reduction of the Nielsen fixed point theorem for symmetric product maps to the Lefschetz theorem, Fund. Math. 135 (1990), 175-176.
  15. [S1] H. Schirmer, An index and a Nielsen number for n-valued multifunctions, Fund. Math. 124 (1984), 207-219.
  16. [S2] H. Schirmer, A minimum theorem for n-valued multifunctions, Fund. Math. 126 (1985), 83-92.
  17. [S3] H. Schirmer, A fixed point index for bimaps, Fund. Math. 134 (1990), 93-104.
  18. [S4] H. Schirmer, The least number of fixed points of bimaps, Fund. Math. 137 (1991), 1-8.
Banach Center Publications
1999/49/1
Export to PBN, Opens in new tab
Pages:
69-75
Main language of publication
English
Published
1999
Exact and natural sciences