| Title:
|
Notes on approximation in the Musielak-Orlicz spaces of vector multifunctions (English) |
| Author:
|
Kasperski, Andrzej |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
35 |
| Issue:
|
1 |
| Year:
|
1994 |
| Pages:
|
81-93 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We introduce the spaces $M^{1}_{Y,\varphi }$, $M^{o,n}_{Y,\varphi }$, $\tilde{M}^{o}_{Y,\varphi }$ and $M^{o}_{Y,\bold d,\varphi }$ of multifunctions. We prove that the spaces $M^{1}_{Y,\varphi }$ and $M^{o}_{Y,\bold d,\varphi }$ are complete. Also, we get some convergence theorems. (English) |
| Keyword:
|
Musielak-Orlicz space |
| Keyword:
|
multifunction |
| Keyword:
|
modular space of multifunctions |
| Keyword:
|
integral operator |
| Keyword:
|
modular approximation |
| MSC:
|
28B20 |
| MSC:
|
46A80 |
| MSC:
|
46E30 |
| MSC:
|
46E99 |
| idZBL:
|
Zbl 0809.46022 |
| idMR:
|
MR1292585 |
| . |
| Date available:
|
2009-01-08T18:08:55Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118643 |
| . |
| Reference:
|
[1] Kasperski A.: Modular approximation in $\utilde{X}_{\varphi }$ by a filtered family of dist-sublinear operators and dist-convex operators.Mathematica Japonica 38 (1993), 119-125. MR 1204190 |
| Reference:
|
[2] Kasperski A.: Notes on approximation in the Musielak-Orlicz spaces of multifunctions.Commentationes Math., in print. |
| Reference:
|
[3] Musielak J.: Modular approximation by a filtered family of linear operators.Functional Analysis and Approximation, Proc. Conf. Oberwolfach, August 9-16, 1980; Birkhäuser Verlag, Basel, 1981, pp. 99-110. Zbl 0471.46017, MR 0650267 |
| Reference:
|
[4] Musielak J.: Orlicz spaces and Modular spaces.Lecture Notes in Mathematics Vol. 1034, Springer-Verlag, Berlin, 1983. Zbl 0557.46020, MR 0724434 |
| Reference:
|
[5] Wisła M.: On completeness of Musielak-Orlicz spaces.Chin. Ann. of Math. 10B(3) (1989), 292-300. MR 1027668 |
| . |
