Convergence of iterative algorithms for multivalued mappings in Banach spaces

We show strong and weak convergence for Mann iteration of multivalued nonexpansive mappings TT in a Banach space. Furthermore, we give a strong convergence of the modified Mann iteration which is independent of the convergence of the implicit anchor-like continuous path zt∈tu+(1−t)Tztzt∈tu+(1−t)Tzt.