| Title:
|
The multicores in metric spaces and their application in fixed point theory (English) |
| Author:
|
Ślosarski, Mirosław |
| Language:
|
English |
| Journal:
|
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica |
| ISSN:
|
0231-9721 |
| Volume:
|
49 |
| Issue:
|
1 |
| Year:
|
2010 |
| Pages:
|
75-94 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
This paper discusses the notion, the properties and the application of multicores, i.e. some compact sets contained in metric spaces. (English) |
| Keyword:
|
Lefschetz number |
| Keyword:
|
fixed point |
| Keyword:
|
topological vector spaces |
| Keyword:
|
Klee admissible spaces |
| Keyword:
|
absolute neighborhood multi-retracts |
| Keyword:
|
approximative absolute neighborhood multi-retracts |
| Keyword:
|
multicore |
| MSC:
|
47H10 |
| MSC:
|
54C55 |
| MSC:
|
54H25 |
| MSC:
|
55M20 |
| idZBL:
|
Zbl 1253.55002 |
| idMR:
|
MR2797525 |
| . |
| Date available:
|
2010-09-13T06:58:01Z |
| Last updated:
|
2013-09-18 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140739 |
| . |
| Reference:
|
[1] Agarwal, G. P., O’Regan, D.: A note on the Lefschetz fixed point theorem for admissible spaces.Bull. Korean Math. Soc. 42, 2 (2005), 307–313. Zbl 1089.47040, MR 2153878, 10.4134/BKMS.2005.42.2.307 |
| Reference:
|
[2] Andres, J., Górniewicz, L.: Topological principles for boundary value problems.Kluwer, Dordrecht, 2003. |
| Reference:
|
[3] Bogatyi, S. A.: Approximative and fundamental retracts.Math. USSR Sb. 22 (1974), 91–103. MR 0336695, 10.1070/SM1974v022n01ABEH001687 |
| Reference:
|
[4] Borsuk, K.: Theory of Shape.Lect. Notes Ser. 28, Matematisk Institut, Aarhus Universitet, Aarhus, 1971. Zbl 0232.55021, MR 0293602 |
| Reference:
|
[5] Clapp, M. H.: On a generalization of absolute neighborhood retracts.Fund. Math. 70 (1971), 117–130. Zbl 0231.54012, MR 0286081 |
| Reference:
|
[6] Eilenberg, S., Steenrod, N.: Foundations of Algebraic Topology.New Jersey Princeton University Press, Princeton, 1952. Zbl 0047.41402, MR 0050886 |
| Reference:
|
[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. Zbl 0294.54034, MR 0339116 |
| Reference:
|
[8] Górniewicz, L.: Topological methods in fixed point theory of multi-valued mappings.Springer, New York–Berlin–Heidelberg, 2006. |
| Reference:
|
[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. Zbl 1031.55002, MR 1962224 |
| Reference:
|
[10] Górniewicz, L., Ślosarski, M.: Once more on the Lefschetz fixed point theorem.Bull. Polish Acad. Sci. Math. 55 (2007), 161–170. Zbl 1122.55002, MR 2318637, 10.4064/ba55-2-7 |
| Reference:
|
[11] Górniewicz, L., Ślosarski, M.: Fixed points of mappings in Klee admissible spaces.Control and Cybernetics 36, 3 (2007). MR 2376056 |
| Reference:
|
[12] Granas, A.: Generalizing the Hopf–Lefschetz fixed point theorem for non-compact ANR’s.In: Symp. Inf. Dim. Topol., Baton-Rouge, 1967. |
| Reference:
|
[13] Granas, A., Dugundji, J.: Fixed Point Theory.Springer, Berlin–Heidelberg–New York, 2003. Zbl 1025.47002, MR 1987179 |
| Reference:
|
[14] Jaworowski, J.: Continuous Homology Properties of Approximative Retracts.Bulletin de L’Academie Polonaise des Sciences 18, 7 (1970). Zbl 0199.26004, MR 0267574 |
| Reference:
|
[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. |
| Reference:
|
[16] Kryszewski, W.: The Lefschetz type theorem for a class of noncompact mappings.Suppl. Rend. Circ. Mat. Palermo 14, 2 (1987), 365–384. Zbl 0641.55002, MR 0920869 |
| Reference:
|
[17] Leray, J., Schauder, J.: Topologie et $\acute{e}$quations fonctionnelles.Ann. Sci. Ecole Norm. Sup. 51 (1934). |
| Reference:
|
[18] Peitgen, H. O.: On the Lefschetz number for iterates of continuous mappings.Proc. AMS 54 (1976), 441–444. Zbl 0316.55006, MR 0391074 |
| Reference:
|
[19] Skiba, R., Ślosarski, M.: On a generalization of absolute neighborhood retracts.Topology and its Applications 156 (2009), 697–709. Zbl 1166.54008, MR 2492955 |
| Reference:
|
[20] Ślosarski, M.: On a generalization of approximative absolute neighborhood retracts.Fixed Point Theory 10, 2 (2009). Zbl 1185.55002, MR 2569006 |
| Reference:
|
[21] Ślosarski, M.: Fixed points of multivalued mappings in Hausdorff topological spaces.Nonlinear Analysis Forum 13, 1 (2008), 39–48. MR 2808029 |
| . |
