Convergence of iterative algorithms for multivalued mappings in Banach spaces

We show strong and weak convergence for Mann iteration of multivalued nonexpansive mappings T$T$ 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)T_zt$z_t\in tu+(1-t)T{z}_t$.