| Title:
|
A generalization of the Schauder fixed point theorem via multivalued contractions (English) |
| Author:
|
Cubiotti, Paolo |
| Author:
|
Di Bella, Beatrice |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
42 |
| Issue:
|
4 |
| Year:
|
2001 |
| Pages:
|
637-640 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We establish a fixed point theorem for a continuous function $f:X\to E$, where $E$ is a Banach space and $X\subseteq E$. Our result, which involves multivalued contractions, contains the classical Schauder fixed point theorem as a special case. An application is presented. (English) |
| Keyword:
|
fixed points |
| Keyword:
|
multivalued contractions |
| Keyword:
|
absolute retracts |
| MSC:
|
47H04 |
| MSC:
|
47H10 |
| idZBL:
|
Zbl 1068.47070 |
| idMR:
|
MR1883372 |
| . |
| Date available:
|
2009-01-08T19:17:02Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119279 |
| . |
| Reference:
|
[1] Aubin J.P., Frankowska H.: Set-Valued Analysis.Birkhäuser, Boston, 1990. Zbl 1168.49014, MR 1048347 |
| Reference:
|
[2] Dugundji J., Granas A.: Fixed Point Theory.Vol. I, PWN - Polish Scientific Publishers, Warsaw, 1982. Zbl 1025.47002, MR 0660439 |
| Reference:
|
[3] Hoffmann A.: The distance to the intersection of two convex sets expressed by the distances to each of them.Math. Nachr. 157 (1992), 81-98. Zbl 0773.52002, MR 1233049 |
| Reference:
|
[4] Klein E., Thompson A.C.: Theory of Correspondences.John Wiley and Sons, New York, 1984. Zbl 0556.28012, MR 0752692 |
| Reference:
|
[5] Ricceri B.: Une propriété topologique de l'ensemble des points fixes d'une contraction multivoque à valeurs convexes.Atti Acc. Lincei Rend. Fis. 81 (8) (1987), 283-286. Zbl 0666.47030, MR 0999821 |
| . |
