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.
@article{118643,
author = {Andrzej Kasperski},
title = {Notes on approximation in the Musielak-Orlicz spaces of vector multifunctions},
journal = {Commentationes Mathematicae Universitatis Carolinae},
volume = {35},
year = {1994},
pages = {81-93},
zbl = {0809.46022},
mrnumber = {1292585},
language = {en},
url = {http://dml.mathdoc.fr/item/118643}
}
Kasperski, Andrzej. Notes on approximation in the Musielak-Orlicz spaces of vector multifunctions. Commentationes Mathematicae Universitatis Carolinae, Tome 35 (1994) pp. 81-93. http://gdmltest.u-ga.fr/item/118643/
Modular approximation in $\utilde{X}_{\varphi }$ by a filtered family of dist-sublinear operators and dist-convex operators, Mathematica Japonica 38 (1993), 119-125. (1993) | MR 1204190
Notes on approximation in the Musielak-Orlicz spaces of multifunctions, Commentationes Math., in print.
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. | MR 0650267 | Zbl 0471.46017
Orlicz spaces and Modular spaces, Lecture Notes in Mathematics Vol. 1034, Springer-Verlag, Berlin, 1983. | MR 0724434 | Zbl 0557.46020
On completeness of Musielak-Orlicz spaces, Chin. Ann. of Math. 10B(3) (1989), 292-300. (1989) | MR 1027668