On the Nielsen fixed point theory for multivalued mappings

Zdzisław Dzedzej

Banach Center Publications (1999)

  • Volume: 49, Issue: 1, page 69-75
  • ISSN: 0137-6934

Abstract

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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.

How to cite

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Dzedzej, Zdzisław. "On the Nielsen fixed point theory for multivalued mappings." Banach Center Publications 49.1 (1999): 69-75. <http://eudml.org/doc/208969>.

@article{Dzedzej1999,
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.},
author = {Dzedzej, Zdzisław},
journal = {Banach Center Publications},
keywords = {ANR; Reidemeister class; Nielsen classes; index theory},
language = {eng},
number = {1},
pages = {69-75},
title = {On the Nielsen fixed point theory for multivalued mappings},
url = {http://eudml.org/doc/208969},
volume = {49},
year = {1999},
}

TY - JOUR
AU - Dzedzej, Zdzisław
TI - On the Nielsen fixed point theory for multivalued mappings
JO - Banach Center Publications
PY - 1999
VL - 49
IS - 1
SP - 69
EP - 75
AB - 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.
LA - eng
KW - ANR; Reidemeister class; Nielsen classes; index theory
UR - http://eudml.org/doc/208969
ER -

References

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  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. Zbl0757.54019
  9. [Je1] J. Jezierski, The Nielsen relation for multivalued maps, Serdica 13 (1987), 174-181. Zbl0652.55004
  10. [Je2] J. Jezierski, An example of finitely-valued fixed point free map, Zesz. Nauk. IM UG 6 (1987), 87-93. Zbl0761.54025
  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. Zbl0712.55003
  13. [Mas] S. Masih, On the fixed point index and Nielsen fixed point theorem for symmetric product mappings, Fund. Math. 102 (1979), 143-158. Zbl0401.55003
  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. Zbl0715.55004
  15. [S1] H. Schirmer, An index and a Nielsen number for n-valued multifunctions, Fund. Math. 124 (1984), 207-219. Zbl0543.55003
  16. [S2] H. Schirmer, A minimum theorem for n-valued multifunctions, Fund. Math. 126 (1985), 83-92. Zbl0609.55001
  17. [S3] H. Schirmer, A fixed point index for bimaps, Fund. Math. 134 (1990), 93-104. Zbl0708.55001
  18. [S4] H. Schirmer, The least number of fixed points of bimaps, Fund. Math. 137 (1991), 1-8. Zbl0726.55001

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