We give results about embeddings, approximation and convergence theorems for a class of general nonlinear operators of integral type in abstract modular function spaces. Thus we extend some previous result on the matter.

The aim of this paper, is to introduce the convex structure (specially, Takahashi convex structure) on modular spaces. Moreover, we are interested in proving some common fixed point theorems for non-self mappings in modular space.

We introduce the spaces $M_{Y,\varphi }^1$, $M_{Y,\varphi }^{o,n}$, ${\tilde{M}}_{Y,\varphi }^o$ and $M_{Y,𝐝,\varphi }^o$ of multifunctions. We prove that the spaces $M_{Y,\varphi }^1$ and $M_{Y,𝐝,\varphi }^o$ are complete. Also, we get some convergence theorems.