Abstract:We introduced the notion of $({\bold X},\dist ,{\Cal V})$-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.
Keywords: Musielak-Orlicz space, multifunction, modular space of multifunctions, approximation, singular kernel
AMS Subject Classification: 54C60, 28B20