| Title:
|
Fixed points for multifunctions on generalized metric spaces with applications to a multivalued Cauchy problem (English) |
| Author:
|
Petruşel, Adrian |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
38 |
| Issue:
|
4 |
| Year:
|
1997 |
| Pages:
|
657-663 |
| . |
| Category:
|
math |
| . |
| Summary:
|
The purpose of this paper is to prove an existence result for a multivalued Cauchy problem using a fixed point theorem for a multivalued contraction on a generalized complete metric space. (English) |
| Keyword:
|
generalized metric space |
| Keyword:
|
multivalued contraction |
| Keyword:
|
fixed points |
| MSC:
|
34A12 |
| MSC:
|
34A60 |
| MSC:
|
47H10 |
| MSC:
|
47N20 |
| MSC:
|
54C60 |
| MSC:
|
54H25 |
| idZBL:
|
Zbl 0938.34005 |
| idMR:
|
MR1603686 |
| . |
| Date available:
|
2009-01-08T18:37:08Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118964 |
| . |
| Reference:
|
[1] Aubin J.P., Cellina A.: Differential Inclusions.Springer Verlag, Berlin, 1984. Zbl 0538.34007, MR 0755330 |
| Reference:
|
[2] Aumann R.J.: Integrals of set-valued functions.J. Math. Anal. Appl. 12 (1965), 1-12. Zbl 0163.06301, MR 0185073 |
| Reference:
|
[3] Covitz H., Nadler S.B., Jr.: Multivalued contraction mappings in generalized metric spaces.Israel J. Math. 8 (1970), 5-11. MR 0263062 |
| Reference:
|
[4] Hiai F., Umegake H.: Integrals, conditional expectations and martingales of multivalued functions.J. Multivariate Anal. 7 (1977), 149-182. MR 0507504 |
| Reference:
|
[5] Himmelberg C.J., Van Vleck F.S.: Lipschitzian generalized differential equations.Rend. Sem. Mat. Univ. Parma 48 (1973), 159-169. Zbl 0289.49009, MR 0340692 |
| Reference:
|
[6] Jung C.K.: On generalized complete metric space.Bull. A.M.S. 75 (1969), 113-116. MR 0234446 |
| Reference:
|
[7] Kisielewicz M.: Differential Inclusions and Optimal Control.Kluwer Acad. Publ., Dordrecht, 1991. MR 1135796 |
| Reference:
|
[8] Kuratowski K., Ryll-Nardzewski C.: A general theorem on selectors.Bull. Polish Acad. Sci. 13 (1965), 397-403. Zbl 0152.21403, MR 0188994 |
| Reference:
|
[9] Luxemburg W.A.J.: On the convergence of successive approximations in the theory of ordinary differential equations, II.Indag. Math. 20 (1958), 540-546. MR 0124554 |
| Reference:
|
[10] Petruşel A.: On a theorem by Roman Wegrzyk.Demonstratio Math. 29 (1996), 637-641. MR 1415506 |
| Reference:
|
[11] Wegrzyk R.: Fixed point theorems for multivalued functions and their applications to functional equations.Diss. Math. 201 (1982), 1-28. MR 0687277 |
| . |
