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The equivalence between the convergences of Ishikawa and Mann iterations for an asymptotically pseudocontractive map. (English) Zbl 1045.47057
In this paper, it is shown that the convergence of Mann iterations is equivalent to the convergence of Ishikawa iterations for asymptotically nonexpansive and asymptotically pseudocontractive mappings, using essentially the technique of B. E. Rhoades and Ş. M. Şoltuz [Int. J. Math. Math. Sci. 2003, 2645–2651 (2003; Zbl 1045.47058), see the following review]. In a similar fashion, one can show that the converence of Mann-Ishikawa iterations is equivalent to the convergence of three-step (Noor) iterations [see M. Aslam Noor, J. Math. Anal. Appl. 251, 217–229 (2000; Zbl 0964.49007)].

MSC:
47J25Iterative procedures (nonlinear operator equations)
47H10Fixed point theorems for nonlinear operators on topological linear spaces
47H09Mappings defined by “shrinking” properties