Abstract: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.
Keywords: Musielak-Orlicz space, multifunction, modular space of multifunctions, integral operator, modular approximation
AMS Subject Classification: 46E99, 28B20