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ArticleOriginal scientific text

Title

Locally admissible multi-valued maps

Authors 1

Affiliations

  1. Technical University of Koszalin, Śniadeckich 2, 75-453 Koszalin, Poland

Abstract

In this paper we generalize the class of admissible mappings as due by L. Górniewicz in 1976. Namely we define the notion of locally admissible mappings. Some properties and applications to the fixed point problem are presented.

Keywords

ENG
Lefschetz number, fixed point, absolute neighborhood multi-retracts, admissible maps, locally admissible maps

Bibliography

  1. G.P. Agarwal and D. O'Regan, A note on the Lefschetz fixed point theorem for admissible spaces, Bull. Korean Math. Soc. 42 (2) (2005), 307-313. doi: 10.4134/BKMS.2005.42.2.307
  2. J. Andres and L. Górniewicz, Topological principles for boundary value problems, Kluwer, 2003.
  3. S.A. Bogatyi, Approximative and fundamental retracts, Math. USSR Sb. 22 (1974), 91-103. doi: 10.1070/SM1974v022n01ABEH001687
  4. S. Eilenberg and D. Montomery, Fixed points theorems for multi-valued transformations, Amer. J. Math. 58 (1946), 214-222. doi: 10.2307/2371832
  5. L. Górniewicz, Topological methods in fixed point theory of multi-valued mappings, Springer, 2006.
  6. L. Górniewicz and D. Rozpłoch-Nowakowska, The Lefschetz fixed point theory for morphisms in topological vector spaces, Topological Methods in Nonlinear Analysis, Journal of the Juliusz Schauder Center 20 (2002), 315-333. doi: 10.7151/dmdico.1130
  7. L. Górniewicz and M. Ślosarski, Once more on the Lefschetz fixed point theorem, Bull. Polish Acad. Sci. Math. 55 (2007), 161-170.
  8. L. Górniewicz and M. Ślosarski, Fixed points of mappings in Klee admissible spaces, Control and Cybernetics 36 (3) (2007), 825-832. doi: 10.4064/ba55-2-7
  9. A. Granas, Generalizing the Hopf- Lefschetz fixed point theorem for non-compact ANR's, in: Symp. Inf. Dim. Topol., Baton-Rouge, 1967.
  10. A. Granas and J. Dugundji, Fixed Point Theory, Springer, 2003.
  11. J. Leray and J. Schauder, Topologie et équations fonctionnelles, Ann. Sci. Ecole Norm. Sup. 51 (1934).
  12. H.O. Peitgen, On the Lefschetz number for iterates of continuous mappings, Proc. AMS 54 (1976), 441-444.
  13. R. Skiba and M. Ślosarski, On a generalization of absolute neighborhood retracts, Topology and its Applications 156 (2009), 697-709. doi: 10.1016/j.topol.2008.09.007
  14. M. Ślosarski, On a generalization of approximative absolute neighborhood retracts, Fixed Point Theory 10 (2) (2009), 329-346.
  15. M. Ślosarski, Fixed points of multivalued mappings in Hausdorff topological spaces, Nonlinear Analysis Forum 13 (1) (2008), 39-48.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
2011/31/1
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Pages:
115-132
Main language of publication
English
Received
2010-05-26
Published
2011

DOI: 10.7151/dmdico.1130

Exact and natural sciences