| Title:
|
Fixed point theorems for weakly sequentially closed maps (English) |
| Author:
|
O'Regan, Donal |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
36 |
| Issue:
|
1 |
| Year:
|
2000 |
| Pages:
|
61-70 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A number of fixed point theorems are presented for weakly contractive maps which have weakly sequentially closed graph. Our results automatically lead to new existence theorems for differential inclusions in Banach spaces relative to the weak topology. (English) |
| Keyword:
|
fixed points |
| Keyword:
|
weakly sequentially closed maps |
| Keyword:
|
weakly contractive maps |
| MSC:
|
34G25 |
| MSC:
|
47H10 |
| MSC:
|
47J05 |
| idZBL:
|
Zbl 1049.47051 |
| idMR:
|
MR1751614 |
| . |
| Date available:
|
2008-06-06T22:25:14Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107718 |
| . |
| Reference:
|
[1] Aliprantis C. D., Border K. C.: Infinite dimensional analysis.Springer-Verlag Berlin, 1985. |
| Reference:
|
[2] Arino O., Gautier S., Penot J. P.: A fixed point theorem for sequentially continuous mappings with applications to ordinary differential equations.Funkc. Ekvac. 27 (1984), 273–279. MR 0794756 |
| Reference:
|
[3] Chow S. N., Schuur J. D.: An existence theorem for ordinary differential equations in Banach spaces.Bull. Amer. Math. Soc. 77 (1971), 1018–1020. Zbl 0264.34072, MR 0287127 |
| Reference:
|
[4] Chow S. N., Schuur J. D.: Fundamental theory of contingent differential equations in Banach spaces.Trans. Amer. Math. Soc. 179 (1973), 133–144. MR 0324162 |
| Reference:
|
[5] Cichoń M.: Weak solutions of differential equations in Banach spaces.Discuss. Mathematicae–Differential Inclusions, 15 (1995), 5–14. MR 1344523 |
| Reference:
|
[6] Edwards R. E.: Functional analysis, theory and applications.Holt, Rinehart and Winston, New York, 1965. Zbl 0182.16101, MR 0221256 |
| Reference:
|
[7] Geitz R. F.: Pettis integration.Proc. Amer. Math. Soc. 82 (1981), 81–86. Zbl 0506.28007, MR 0603606 |
| Reference:
|
[8] Himmelberg C. J.: Fixed points of compact multifunctions.Jour. Math. Anal. Appl. 38 (1972), 205–207. Zbl 0225.54049, MR 0303368 |
| Reference:
|
[9] Köthe G.: Topological vector spaces I.Springer-Verlag Berlin, 1965. MR 0551623 |
| Reference:
|
[10] Mitchell A. R., Smith C. K. L.: An existence theorem for weak solutions of differential equations in Banach spaces.In: Nonlinear Equations in Abstract Spaces (edited by V. Lakshmikantham), Academic Press (1978), 387–404. Zbl 0452.34054, MR 0502554 |
| Reference:
|
[11] O’Regan D.: Integral equations in reflexive Banach spaces and weak topologies.Proc. Amer. Math. Soc. 124 (1996), 607–614. MR 1301043 |
| Reference:
|
[12] O’Regan D.: Fixed point theory for weakly sequentially continuous mappings.Mathematical and Computer Modelling 27(5) (1998), 1–14. Zbl 1185.34026, MR 1616796 |
| Reference:
|
[13] O’Regan D.: Weak solutions of ordinary differential equations in Banach spaces.Applied Math. Letters 12(1) (1999), 101–105. Zbl 0933.34068, MR 1663477 |
| Reference:
|
[14] O’Regan D.: Fixed point theory for weakly contractive maps with applications to operator inclusions in Banach spaces relative to the weak topology.Zeitschrift für Analysis und ihre Anwendungen 17 (1998), 282–296. Zbl 0911.47057, MR 1632523 |
| Reference:
|
[15] O’Regan D.: Nonlinear operator approximation theory.Numerical Functional Analysis and Optimization 19(5/6) (1998), 587–592. MR 1636474 |
| Reference:
|
[16] Smith C. K. L.: Measure of nonconvergence and noncompactness.Ph.D thesis, University of Texas at Arlington, 1978. MR 2628255 |
| Reference:
|
[17] Szep A.: Existence theorems for weak solutions of ordinary differential equations in reflexive Banach spaces.Studia Sci. Math. Hungar. 6 (1971), 197–203. MR 0330688 |
| . |
