| Title:
|
Notes on approximation in the Musielak-Orlicz sequence spaces of multifunctions (English) |
| Author:
|
Kasperski, Andrzej |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
36 |
| Issue:
|
1 |
| Year:
|
1995 |
| Pages:
|
19-24 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We introduced the notion of $({\bold X},\operatorname{dist},{\Cal V})$-boundedness of a filtered family of operators in the Musielak-Orlicz sequence space $X_{\varphi }$ of multifunctions. This notion is used to get the convergence theorems for the families of ${\bold X}$-linear operators, ${\bold X}$-dist-sublinear operators and ${\bold X}$-dist-convex operators. Also, we prove that $X_{\varphi }$ is complete. (English) |
| Keyword:
|
Musielak-Orlicz space |
| Keyword:
|
multifunction |
| Keyword:
|
modular space of multifunctions |
| Keyword:
|
approximation |
| Keyword:
|
singular kernel |
| MSC:
|
28B20 |
| MSC:
|
41A65 |
| MSC:
|
46E30 |
| MSC:
|
54C60 |
| idZBL:
|
Zbl 0832.54021 |
| idMR:
|
MR1334410 |
| . |
| Date available:
|
2009-01-08T18:15:43Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118728 |
| . |
| Reference:
|
[1] Kasperski A.: Modular approximation by a filtered family of sublinear operators.Commentationes Math. XXVII (1987), 109-114. Zbl 0636.46025, MR 0910964 |
| Reference:
|
[2] Kasperski A.: Modular approximation in $\utilde{X}_{\varphi }$ by a filtered family of $\utilde{X}_{\varphi }$-linear operators.Functiones et Approximatio XX (1992), 183-187. MR 1201727 |
| Reference:
|
[3] 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:
|
[4] Kasperski A.: Approximation of elements of the spaces $X^{1}_{\varphi }$ and $X_{\varphi }$ by nonlinear singular kernels.Annales Math. Silesianae, Vol. 6, Katowice, 1992, pp. 21-29. Zbl 0821.41021, MR 1217338 |
| Reference:
|
[5] Kasperski A.: Notes on approximation in the Musielak-Orlicz space of multifunctions.Commentationes Math., in print. |
| Reference:
|
[6] Musielak J.: Modular approximation by a filtered family of linear operators.``Functional Analysis and Approximation, Proc. Conf. Oberwolfach, August 9-16, 1980'', BirkhäuserVerlag, Basel 1981, pp. 99-110. Zbl 0471.46017, MR 0650267 |
| Reference:
|
[7] Musielak J.: Orlicz Spaces and Modular Spaces.Lecture Notes in Mathematics, Vol. 1034, Springer-Verlag, Berlin, 1983. Zbl 0557.46020, MR 0724434 |
| . |
