Geodesic
Notes on approximation in the Musielak-Orlicz sequence spaces of multifunctions
Commentationes Mathematicae Universitatis Carolinae, Tome 36 (1995) no. 1, pp. 19-24 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 28B20, 41A65, 46E30, 54C60
Keywords: Musielak-Orlicz space; multifunction; modular space of multifunctions; approximation; singular kernel 
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     title = {Notes on approximation in the {Musielak-Orlicz} sequence spaces of multifunctions},
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     year = {1995},
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Kasperski, Andrzej. Notes on approximation in the Musielak-Orlicz sequence spaces of multifunctions. Commentationes Mathematicae Universitatis Carolinae, Tome 36 (1995) no. 1, pp. 19-24. http://geodesic.mathdoc.fr/item/CMUC_1995_36_1_a4/