The equivalence of Mann iteration and Ishikawa iteration for non-Lipschitzian operators (Q1415119)

It is shown that the convergence of Mann iteration (one-step) is equivalent to the convergence of Ishikawa (two-step) iteration for various classes of non-Lipschitzian operators. Using essentially the technique of this paper, one can prove that the convergence of Mann-Ishikawa iteration is equivalent to the convergence of three-step iterations, which are known as Noor iteraions for non-Lipschitzian operators. Note that Noor iterations [introduced by \textit{M. Aslam Noor}, J. Math. Anal. Appl. 251, 217--229 (2000; Zbl 0964.49007)] include Mann-Ishikawa iterations as special cases.