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Weak and Strong Convergence of Iterative Algorithm with Errors for Three Asymptotically Nonexpansive Mappings

Construction of fixed points for asymptotically quasi-nonexpansive mappings is one of the important subjects in theory of nonexpansive mappings. Asymptotically quasi-nonexpansive mappings are widely used in a number of applied areas, such as image recovery and signal processing, etc. Consequently, considerable research efforts have been devoted to the study of iterative algorithms for finding fixed points for nonexpansive mappings. Mann iteration method and Ishikawa iteration method are among the most basic and famous iterative methods. In this paper, by combining the idea of Mann iteration and Ishikawa iteration, an iterative algorithm with errors involving three different asymptotically nonexpansive mappings is presented. And, under some conditions, the results that the algorithm converges weakly or strongly to the common fixed points of these three mappings in a uniformly convex Banach space are obtained.