  In this work, a new concept of nonself total asymptotically nonexpansive
mapping is introduced and an iterative process is considered for two nonself
totally asymptotically nonexpansive mappings. Weak and strong convergence
theorems for computing common fixed points of two nonself total asymptotically
nonexpansive mappings are established in the framework of Banach spaces.
Finally, we give an example which show that our theorems are applicable.
