In this interesting paper, the authors consider the equivalence between the one-step, two-step, three-step and multistep-iteration process for solving the nonlinear operator equations
in a Banach space for pseudocontractive operators
. It is worth mentioning that three-step iterative schemes were introduced by M. A. Noor
[J. Math. Anal. Appl. 251, 217–229 (2000; Zbl 0964.49007
)]. Three-step iterations are usually called Noor iterations. The present authors also discuss the stability problems for these iterations. An open problem is also mentioned. Is there a map for which, namely: Noor iteration converges to a fixed point, but for which the Ishikawa iteration fails to converge?