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Keywords:
Musielak-Orlicz space; multifunction; modular space of multifunctions; integral operator; modular approximation
Musielak-Orlicz space; multifunction; modular space of multifunctions; integral operator; modular approximation
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.
References:
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[2] Kasperski A.: Notes on approximation in the Musielak-Orlicz spaces of multifunctions. Commentationes Math., in print.
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[4] Musielak J.: Orlicz spaces and Modular spaces. Lecture Notes in Mathematics Vol. 1034, Springer-Verlag, Berlin, 1983. MR 0724434 | Zbl 0557.46020
[5] Wisła M.: On completeness of Musielak-Orlicz spaces. Chin. Ann. of Math. 10B(3) (1989), 292-300. MR 1027668
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