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The purpose of this paper is to study the weak and strong convergence of an new implicit iteration process to a common fixed point for a finite family of asymptotically nonexpansive mappings in Banach spaces. The results presented in this paper extend and improve important known results in [Bauschke, J. Math. Anal. Appl. 202: 150–159, 1996], [Chang, Cho, Nonlinear Anal. Appl. 1: 369–382, 2003], [Goebel, Kirk, Proc. Amer. Math. Soc. 35: 171–174, 1972]–[Reich, J. Math. Anal. Appl. 75: 287–292, 1980], [Sun, J. Math. Anal. Appl. 286: 351–358, 2003]–[Zhou, Chang, Numer. Funct. Anal. Optim. 23: 911–921, 2002] and others.

Strong and Weak Convergence of Implicit Iterative Process with Errors for Asymptotically Nonexpansive Mappings