Notes on approximation in the Musielak-Orlicz spaces of vector multifunctions
Commentationes Mathematicae Universitatis Carolinae (1994)
- Volume: 35, Issue: 1, page 81-93
- ISSN: 0010-2628
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topKasperski, Andrzej. "Notes on approximation in the Musielak-Orlicz spaces of vector multifunctions." Commentationes Mathematicae Universitatis Carolinae 35.1 (1994): 81-93. <http://eudml.org/doc/247625>.
@article{Kasperski1994,
abstract = {We introduce the spaces $M^\{1\}_\{Y,\varphi \}$, $M^\{o,n\}_\{Y,\varphi \}$, $\tilde\{M\}^\{o\}_\{Y,\varphi \}$ and $M^\{o\}_\{Y,\mathbf \{d\},\varphi \}$ of multifunctions. We prove that the spaces $M^\{1\}_\{Y,\varphi \}$ and $M^\{o\}_\{Y,\mathbf \{d\},\varphi \}$ are complete. Also, we get some convergence theorems.},
author = {Kasperski, Andrzej},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Musielak-Orlicz space; multifunction; modular space of multifunctions; integral operator; modular approximation; Musielak-Orlicz space; modular space of multifunctions; integral operator; modular approximation; spaces of multifunctions; convergence theorems},
language = {eng},
number = {1},
pages = {81-93},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Notes on approximation in the Musielak-Orlicz spaces of vector multifunctions},
url = {http://eudml.org/doc/247625},
volume = {35},
year = {1994},
}
TY - JOUR
AU - Kasperski, Andrzej
TI - Notes on approximation in the Musielak-Orlicz spaces of vector multifunctions
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1994
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 35
IS - 1
SP - 81
EP - 93
AB - We introduce the spaces $M^{1}_{Y,\varphi }$, $M^{o,n}_{Y,\varphi }$, $\tilde{M}^{o}_{Y,\varphi }$ and $M^{o}_{Y,\mathbf {d},\varphi }$ of multifunctions. We prove that the spaces $M^{1}_{Y,\varphi }$ and $M^{o}_{Y,\mathbf {d},\varphi }$ are complete. Also, we get some convergence theorems.
LA - eng
KW - Musielak-Orlicz space; multifunction; modular space of multifunctions; integral operator; modular approximation; Musielak-Orlicz space; modular space of multifunctions; integral operator; modular approximation; spaces of multifunctions; convergence theorems
UR - http://eudml.org/doc/247625
ER -
References
top- Kasperski A., Modular approximation in by a filtered family of dist-sublinear operators and dist-convex operators, Mathematica Japonica 38 (1993), 119-125. (1993) MR1204190
- Kasperski A., Notes on approximation in the Musielak-Orlicz spaces of multifunctions, Commentationes Math., in print.
- 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. Zbl0471.46017MR0650267
- Musielak J., Orlicz spaces and Modular spaces, Lecture Notes in Mathematics Vol. 1034, Springer-Verlag, Berlin, 1983. Zbl0557.46020MR0724434
- Wisła M., On completeness of Musielak-Orlicz spaces, Chin. Ann. of Math. 10B(3) (1989), 292-300. (1989) MR1027668
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