| Title:
|
A finite dimensional reduction of the Schauder Conjecture (English) |
| Author:
|
De Pascale, Espedito |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
34 |
| Issue:
|
3 |
| Year:
|
1993 |
| Pages:
|
401-404 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Schauder's Conjecture (i.e\. every compact convex set in a Hausdorff topological vector space has the f.p.p.) is reduced to the search for fixed points of suitable multivalued maps in finite dimensional spaces. (English) |
| Keyword:
|
compact convex set |
| Keyword:
|
fixed point property |
| Keyword:
|
multivalued map |
| Keyword:
|
local convexity |
| Keyword:
|
topological vector space |
| Keyword:
|
Schauder Conjecture. |
| MSC:
|
46A16 |
| MSC:
|
47H04 |
| MSC:
|
47H10 |
| MSC:
|
54C60 |
| MSC:
|
54H25 |
| idZBL:
|
Zbl 0805.47056 |
| idMR:
|
MR1243070 |
| . |
| Date available:
|
2009-01-08T18:04:35Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118595 |
| . |
| Reference:
|
[1] Aubin J.P., Frankowska H.: Set-Valued Analysis.Birkhäuser, 1990. Zbl 1168.49014, MR 1048347 |
| Reference:
|
[2] Borisovich Yu.G., Gel'man B.D., Myshkis A.D., Obukhovskii V.V.: Topological methods in the theory of fixed points of multivalued mappings.Russian Math. Surveys 35 (1980), 65-143. MR 0565568 |
| Reference:
|
[3] Borisovich Yu.G., Gel'man B.D., Myshkis A.D., Obukhovskii V.V.: Multivalued mappings.J. Sov. Math. (1984), 719-791. |
| Reference:
|
[4] Bourgin D.G.: A degree for nonacyclic multiple-valued transformation.Bull. Amer. Math. Soc. 80 (1974), 59-61. MR 0326505 |
| Reference:
|
[5] Bourgin D.G.: A generalization of the mapping degree.Can. J. Math. 26 (1974), 1109-1117. Zbl 0303.55004, MR 0365552 |
| Reference:
|
[6] Connelly R.: An extension of Brower's fixed-point theorem to nonacyclic, set-valued functions.Proc. Amer. Math. Soc. 43 (1974), 214-218. MR 0339144 |
| Reference:
|
[7] Dzedzey Z.: Fixed point index theory for a class of nonacyclic multivalued maps.Diss. Math. CCLIII (1985). |
| Reference:
|
[8] Eilenberg S., Montgomery D.: Fixed point theorems for multivalued transformations.Amer. J. Math. 58 (1946), 214-222. Zbl 0060.40203, MR 0016676 |
| Reference:
|
[9] Fan K.: Sur un théorème minimax.C. R. Acad. Sci. Paris, Groupe 1, 259 (1962), 3925-3928. MR 0174955 |
| Reference:
|
[10] Gorniewicz L.: Fixed point theorems for multivalued maps of subsets of Euclidean spaces.Bull. Pol. Acad. Sci., Math. 27 (1979), 111-115. MR 0539341 |
| Reference:
|
[11] Granas A.: K K M-maps and their applications to non linear problems.see 16, 45-61. |
| Reference:
|
[12] Hadžic O.: Fixed point theory in topological vector spaces.University of Novi Sad, Novi Sad, 1984. MR 0789224 |
| Reference:
|
[13] Idzik A.: On $\gamma-$almost fixed point theorems. The single valued case.Bull. Pol. Acad. Sci. Math. 35 (1987), 461-464. Zbl 0663.47036, MR 0939008 |
| Reference:
|
[14] Kalton N.J.: An $F$-space with trivial dual where the Krein-Milman theorem holds.Israel J. Math. 36 (1980), 41-49. Zbl 0439.46022, MR 0589656 |
| Reference:
|
[15] Krauthausen C.: Der Fixpunktsatz von Schauder in nicht notwendig Konvexen Räumen sowie Anwendungen auf Hammerstein'sche Gleichungen.Dissertation, TH Aachen, 1976. |
| Reference:
|
[16] Mauldin R.D. editor: The Scottish Book.Birkhäuser, 1981. MR 0666400 |
| Reference:
|
[17] O'Neill B.: A fixed point theorem for multivalued functions.Duke Math. J. 24 (1957), 61-62. |
| Reference:
|
[18] O'Neill B.: Induced homology homomorphism for set-valued maps.Pac. J. Math. 7 (1957), 1179-1184. MR 0104226 |
| Reference:
|
[19] Powers M.J.: Lefschetz fixed point theorems for a new class of multivalued maps.Pac. J. Math. 42 (1972), 211-220. MR 0334189 |
| Reference:
|
[20] Schauder J.: Der Fixpunktsatz in Funktionalräumen.Studia Math. 2 (1930), 171-180. |
| Reference:
|
[21] Tychonoff A.: Ein Fixpunktsatz.Math. Ann. 111 (1935), 767-776. Zbl 0012.30803, MR 1513031 |
| Reference:
|
[22] Weber H.: Compact convex sets in non locally convex linear spaces.to appear in Note Mat., 1992. Zbl 0846.46004, MR 1258580 |
| . |
