| Title:
|
On local and global injectivity of noncompact vector fields in non necessarily locally convex vector spaces (English) |
| Author:
|
Alex, Holger |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
35 |
| Issue:
|
2 |
| Year:
|
1994 |
| Pages:
|
239-248 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We give in this paper conditions for a mapping to be globally injective in a topological vector space. (English) |
| Keyword:
|
fixed point index |
| Keyword:
|
locally injective mappings |
| Keyword:
|
$(\varphi, \gamma )$-condensing mappings |
| MSC:
|
47H09 |
| MSC:
|
47H10 |
| MSC:
|
47H11 |
| MSC:
|
47e10 |
| idZBL:
|
Zbl 0815.47073 |
| idMR:
|
MR1286570 |
| . |
| Date available:
|
2009-01-08T18:10:36Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118662 |
| . |
| Reference:
|
[1] Alex H., Hahn S., Kaniok L.: The fixed point index for noncompact mappings in non locally convex topological vector spaces.Comment. Math. Univ. Carolinae 35 (1994), 249-257. Zbl 0807.47038, MR 1286571 |
| Reference:
|
[2] Alex H., Hahn S.: On the uniqueness of the fixed point in the Schauder fixed point theorem.Radovi Mathematicki 6 (1990), 265-271. Zbl 0724.47031, MR 1096708 |
| Reference:
|
[3] Banach S., Mazur S.: Über mehrdeutige stetige Abbildungen.Studia Math. 5 (1934), 174-178. |
| Reference:
|
[4] Deimling K.: Nonlinear Functional Analysis.Springer Verlag, Berlin-Heidelberg-New YorkTokyo, 1985. Zbl 0559.47040, MR 0787404 |
| Reference:
|
[5] Hadzic O.: Fixed Point Theory in Topological Vector Spaces.Novi Sad, 1984. Zbl 0576.47030, MR 0789224 |
| Reference:
|
[6] Hadzic O.: Some properties of measures of noncompactness in paranormed spaces.Proc. Amer. Math. Soc. 102 (1988), 843-849. Zbl 0653.47034, MR 0934854 |
| Reference:
|
[7] Hahn S.: Gebietsinvarianzsatz und Eigenwertaussagen für konzentrierende Abbildungen.Comment. Math. Univ. Carolinae 18 (1977), 697-713. Zbl 0375.47029, MR 0474385 |
| Reference:
|
[8] Hahn S.: Homöomorphieaussagen für $k$-verdichtende Vektorfelder.Comment. Math. Univ. Carolinae 21 (1980), 563-572. Zbl 0452.47061, MR 0590135 |
| Reference:
|
[9] Hahn S.: Fixpunktsätze für limeskompakte Abbildungen in nicht notwendig lokalkonvexen topologischen Vektorräumen.Comment. Math. Univ. Carolinae 27 (1986), 189-204. MR 0843430 |
| Reference:
|
[10] Kaniok L.: On measures of noncompactness in general topological vector spaces.Comment. Math. Univ. Carolinae 31 (1990), 479-487. Zbl 0738.47051, MR 1078482 |
| Reference:
|
[11] Kellogg R.B: Uniqueness in the Schauder fixed point theorem.Proc. Amer. Math. Soc. 60 (1976), 207-210. MR 0423137 |
| Reference:
|
[12] Plastock R.: Homeomorphisms between Banach spaces.Trans. Amer. Math. Soc. 200 (1974), 169-183. Zbl 0291.54009, MR 0356122 |
| Reference:
|
[13] Riedrich T.: Vorlesungen über nichtlineare Operatorengleichungen.Teubner-Texte zur Mathematik, Leipzig, 1976. Zbl 0332.47026, MR 0467414 |
| Reference:
|
[14] Rinow W.: Lehrbuch der Topologie.Berlin, 1975. Zbl 0317.54001, MR 0514884 |
| Reference:
|
[15] Smith H.L., Stuart C.A.: A uniqueness theorem for fixed points.Proc. Amer. Math. Soc. 79 (1980), 237-240. Zbl 0438.47055, MR 0565346 |
| Reference:
|
[16] Talmann L.A.: A note on Kellogg's uniqueness theorem for fixed points.Proc. Amer. Math. Soc. 69 (1978), 248-250. MR 0467416 |
| . |
