In this paper, we first give the modified version of the iteration process of Thakur et al.  which is faster than Picard, Mann, Ishikawa, Noor, Agarwal et al.  and Abbas et al.  processes. Secondly, we prove weak and strong convergence theorems of this iteration process for multivalued quasi nonexpansive mappings in uniformly convex Banach spaces. Thirdly, we support our theorems with analytical examples. Finally, we compare rates of convergence for multivalued version of iteration processes mentioned above via a numerical example.