The multicores in metric spaces and their application in fixed point theory

Mirosław Ślosarski

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica (2010)

  • Volume: 49, Issue: 1, page 75-94
  • ISSN: 0231-9721

Abstract

top
This paper discusses the notion, the properties and the application of multicores, i.e. some compact sets contained in metric spaces.

How to cite

top

Ślosarski, Mirosław. "The multicores in metric spaces and their application in fixed point theory." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 49.1 (2010): 75-94. <http://eudml.org/doc/116479>.

@article{Ślosarski2010,
abstract = {This paper discusses the notion, the properties and the application of multicores, i.e. some compact sets contained in metric spaces.},
author = {Ślosarski, Mirosław},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {Lefschetz number; fixed point; topological vector spaces; Klee admissible spaces; absolute neighborhood multi-retracts; approximative absolute neighborhood multi-retracts; multicore; set-valued map; Lefschetz fixed point theorem; generalized Lefschetz number; Lefschetz endomorphism; absolute neighborhood retract; multicore of a map; fixed point; Klee admissibility},
language = {eng},
number = {1},
pages = {75-94},
publisher = {Palacký University Olomouc},
title = {The multicores in metric spaces and their application in fixed point theory},
url = {http://eudml.org/doc/116479},
volume = {49},
year = {2010},
}

TY - JOUR
AU - Ślosarski, Mirosław
TI - The multicores in metric spaces and their application in fixed point theory
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2010
PB - Palacký University Olomouc
VL - 49
IS - 1
SP - 75
EP - 94
AB - This paper discusses the notion, the properties and the application of multicores, i.e. some compact sets contained in metric spaces.
LA - eng
KW - Lefschetz number; fixed point; topological vector spaces; Klee admissible spaces; absolute neighborhood multi-retracts; approximative absolute neighborhood multi-retracts; multicore; set-valued map; Lefschetz fixed point theorem; generalized Lefschetz number; Lefschetz endomorphism; absolute neighborhood retract; multicore of a map; fixed point; Klee admissibility
UR - http://eudml.org/doc/116479
ER -

References

top
  1. Agarwal, G. P., O’Regan, D., 10.4134/BKMS.2005.42.2.307, Bull. Korean Math. Soc. 42, 2 (2005), 307–313. (2005) Zbl1089.47040MR2153878DOI10.4134/BKMS.2005.42.2.307
  2. Andres, J., Górniewicz, L., Topological principles for boundary value problems, Kluwer, Dordrecht, 2003. (2003) 
  3. Bogatyi, S. A., 10.1070/SM1974v022n01ABEH001687, Math. USSR Sb. 22 (1974), 91–103. (1974) MR0336695DOI10.1070/SM1974v022n01ABEH001687
  4. Borsuk, K., Theory of Shape, Lect. Notes Ser. 28, Matematisk Institut, Aarhus Universitet, Aarhus, 1971. (1971) Zbl0232.55021MR0293602
  5. Clapp, M. H., On a generalization of absolute neighborhood retracts, Fund. Math. 70 (1971), 117–130. (1971) Zbl0231.54012MR0286081
  6. Eilenberg, S., Steenrod, N., Foundations of Algebraic Topology, New Jersey Princeton University Press, Princeton, 1952. (1952) Zbl0047.41402MR0050886
  7. Fournier, G., Granas, A., The Lefschetz fixed point theorem for some classes of non-metrizable spaces, J. Math. Pures et Appl. 52 (1973), 271–284. (1973) Zbl0294.54034MR0339116
  8. Górniewicz, L., Topological methods in fixed point theory of multi-valued mappings, Springer, New York–Berlin–Heidelberg, 2006. (2006) 
  9. Górniewicz, L., Rozpłoch-Nowakowska, D., 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. (2002) Zbl1031.55002MR1962224
  10. Górniewicz, L., Ślosarski, M., 10.4064/ba55-2-7, Bull. Polish Acad. Sci. Math. 55 (2007), 161–170. (2007) Zbl1122.55002MR2318637DOI10.4064/ba55-2-7
  11. Górniewicz, L., Ślosarski, M., Fixed points of mappings in Klee admissible spaces, Control and Cybernetics 36, 3 (2007). (2007) MR2376056
  12. Granas, A., Generalizing the Hopf–Lefschetz fixed point theorem for non-compact ANR’s, In: Symp. Inf. Dim. Topol., Baton-Rouge, 1967. (1967) 
  13. Granas, A., Dugundji, J., Fixed Point Theory, Springer, Berlin–Heidelberg–New York, 2003. (2003) Zbl1025.47002MR1987179
  14. Jaworowski, J., Continuous Homology Properties of Approximative Retracts, Bulletin de L’Academie Polonaise des Sciences 18, 7 (1970). (1970) Zbl0199.26004MR0267574
  15. Krathausen, C., Müller, G., Reinermann, J., Schöneberg, R., New Fixed Point Theorems for Compact and Nonexpansive Mappings and Applications to Hammerstein Equations, Sonderforschungsbereich 72, Approximation und Optimierung, Universität Bonn, preprint no. 92, 1976. (1976) 
  16. Kryszewski, W., The Lefschetz type theorem for a class of noncompact mappings, Suppl. Rend. Circ. Mat. Palermo 14, 2 (1987), 365–384. (1987) Zbl0641.55002MR0920869
  17. Leray, J., Schauder, J., Topologie et e ´ quations fonctionnelles, Ann. Sci. Ecole Norm. Sup. 51 (1934). (1934) 
  18. Peitgen, H. O., On the Lefschetz number for iterates of continuous mappings, Proc. AMS 54 (1976), 441–444. (1976) Zbl0316.55006MR0391074
  19. Skiba, R., Ślosarski, M., On a generalization of absolute neighborhood retracts, Topology and its Applications 156 (2009), 697–709. (2009) Zbl1166.54008MR2492955
  20. Ślosarski, M., On a generalization of approximative absolute neighborhood retracts, Fixed Point Theory 10, 2 (2009). (2009) Zbl1185.55002MR2569006
  21. Ślosarski, M., Fixed points of multivalued mappings in Hausdorff topological spaces, Nonlinear Analysis Forum 13, 1 (2008), 39–48. (2008) MR2808029

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.