Locally admissible multi-valued maps

Mirosław Ślosarski

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (2011)

  • Volume: 31, Issue: 1, page 115-132
  • ISSN: 1509-9407

Abstract

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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.

How to cite

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Mirosław Ślosarski. "Locally admissible multi-valued maps." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 31.1 (2011): 115-132. <http://eudml.org/doc/271162>.

@article{MirosławŚlosarski2011,
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.},
author = {Mirosław Ślosarski},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
keywords = {Lefschetz number; fixed point; absolute neighborhood multi-retracts; admissible maps; locally admissible maps},
language = {eng},
number = {1},
pages = {115-132},
title = {Locally admissible multi-valued maps},
url = {http://eudml.org/doc/271162},
volume = {31},
year = {2011},
}

TY - JOUR
AU - Mirosław Ślosarski
TI - Locally admissible multi-valued maps
JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization
PY - 2011
VL - 31
IS - 1
SP - 115
EP - 132
AB - 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.
LA - eng
KW - Lefschetz number; fixed point; absolute neighborhood multi-retracts; admissible maps; locally admissible maps
UR - http://eudml.org/doc/271162
ER -

References

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  1. [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. [2] J. Andres and L. Górniewicz, Topological principles for boundary value problems, Kluwer, 2003. Zbl1029.55002
  3. [3] S.A. Bogatyi, Approximative and fundamental retracts, Math. USSR Sb. 22 (1974), 91-103. doi: 10.1070/SM1974v022n01ABEH001687 Zbl0301.54042
  4. [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. [5] L. Górniewicz, Topological methods in fixed point theory of multi-valued mappings, Springer, 2006. Zbl1107.55001
  6. [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 Zbl1031.55002
  7. [7] L. Górniewicz and M. Ślosarski, Once more on the Lefschetz fixed point theorem, Bull. Polish Acad. Sci. Math. 55 (2007), 161-170. Zbl1122.55002
  8. [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 Zbl1194.47062
  9. [9] A. Granas, Generalizing the Hopf- Lefschetz fixed point theorem for non-compact ANR's, in: Symp. Inf. Dim. Topol., Baton-Rouge, 1967. 
  10. [10] A. Granas and J. Dugundji, Fixed Point Theory, Springer, 2003. 
  11. [11] J. Leray and J. Schauder, Topologie et équations fonctionnelles, Ann. Sci. Ecole Norm. Sup. 51 (1934). Zbl60.0322.02
  12. [12] H.O. Peitgen, On the Lefschetz number for iterates of continuous mappings, Proc. AMS 54 (1976), 441-444. Zbl0316.55006
  13. [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 Zbl1166.54008
  14. [14] M. Ślosarski, On a generalization of approximative absolute neighborhood retracts, Fixed Point Theory 10 (2) (2009), 329-346. Zbl1185.55002
  15. [15] M. Ślosarski, Fixed points of multivalued mappings in Hausdorff topological spaces, Nonlinear Analysis Forum 13 (1) (2008), 39-48. Zbl1295.54091

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