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In this paper, we introduce an iteration process for approximating common fixed points of two nonself asymptotically nonexpansive map- pings in Banach spaces. Our process contains Mann iteration process and some other processes for nonself mappings but is independent of Ishikawa iteration process. We prove some weak and strong convergence theorems for this iteration process. Our results generalize and improve some results in contemporary literature.doi:10.2478/v10309-012-0002-y fatcat:ajyimxqztzdyjpqn3qynyagi24