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<p>Abstract</p> <p>The purpose of this paper is to introduce two implicit iteration schemes for approximating fixed points of nonexpansive mapping <inline-formula> <graphic file="1687-1812-2008-751383-i1.gif"/></inline-formula> and a finite family of nonexpansive mappings <inline-formula> <graphic file="1687-1812-2008-751383-i2.gif"/></inline-formula>, respectively, in Banach spaces and to prove weak and strong convergence theorems. The results presented in this paper improve and extend the corresponding ones of H.-K. Xu and R. Ori, 2001, Z. Opial, 1967, and others.</p>