# Article

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Keywords:
Musielak-Orlicz space; multifunction; modular space of multifunctions; approximation; singular kernel
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.
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