On the Nielsen fixed point theory for multivalued mappings
Dzedzej, Zdzisław
Banach Center Publications, Tome 50 (1999), p. 69-75 / Harvested from The Polish Digital Mathematics Library
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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.

Publié le : 1999-01-01
EUDML-ID : urn:eudml:doc:208969 
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     author = {Dzedzej, Zdzis\l aw},
     title = {On the Nielsen fixed point theory for multivalued mappings},
     journal = {Banach Center Publications},
     volume = {50},
     year = {1999},
     pages = {69-75},
     zbl = {0942.55004},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv49i1p69bwm}
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Dzedzej, Zdzisław. On the Nielsen fixed point theory for multivalued mappings. Banach Center Publications, Tome 50 (1999) pp. 69-75. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv49i1p69bwm/

[000] [An] J. Andres, Multiple bounded solutions of differential inclusions: The Nielsen theory approach, Preprint (1997).

[001] [AC] J. P. Aubin and A. Cellina, Differential Inclusions, Springer-Verlag, 1984.

[002] [Bro] R. F. Brown, The Lefschetz Fixed Point Theorem, Scott, Foresman & Co., Glenview Ill., 1971.

[003] [Do] A. Dold, Lectures on Algebraic Topology, Springer-Verlag, 1972.

[004] [Dz1] Z. Dzedzej, Fixed point index theory for a class of non-acyclic multivalued maps, Dissertationes Math. 253 (1985).

[005] [Dz2] Z. Dzedzej, On Nielsen and Reidemeister relations for set-valued symmetric product maps, CRM Barcelona 76 (1989), 1-8.

[006] [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.

[007] [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. | Zbl 0757.54019

[008] [Je1] J. Jezierski, The Nielsen relation for multivalued maps, Serdica 13 (1987), 174-181. | Zbl 0652.55004

[009] [Je2] J. Jezierski, An example of finitely-valued fixed point free map, Zesz. Nauk. IM UG 6 (1987), 87-93. | Zbl 0761.54025

[010] [Jia] B. Jiang, Lectures on Nielsen Fixed Point Theory, Contemp. Math. 14, AMS, Providence, R.I., 1983.

[011] [KrM] W. Kryszewski and D. Miklaszewski, The Nielsen number of set-valued maps. An approximation approach, Serdica 15 (1989), 336-344. | Zbl 0712.55003

[012] [Mas] S. Masih, On the fixed point index and Nielsen fixed point theorem for symmetric product mappings, Fund. Math. 102 (1979), 143-158. | Zbl 0401.55003

[013] [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. | Zbl 0715.55004

[014] [S1] H. Schirmer, An index and a Nielsen number for n-valued multifunctions, Fund. Math. 124 (1984), 207-219. | Zbl 0543.55003

[015] [S2] H. Schirmer, A minimum theorem for n-valued multifunctions, Fund. Math. 126 (1985), 83-92. | Zbl 0609.55001

[016] [S3] H. Schirmer, A fixed point index for bimaps, Fund. Math. 134 (1990), 93-104. | Zbl 0708.55001

[017] [S4] H. Schirmer, The least number of fixed points of bimaps, Fund. Math. 137 (1991), 1-8. | Zbl 0726.55001