On the Mann and Ishikawa iteration processes

On the Equivalence of Mann and Ishikawa Iteration Methods

The Mann iterative scheme was invented in 1953, see [7], and was used to obtain convergence to a fixed point for many functions for which the Banach principle fails. For example, the first author in [8] showed that, for any continuous selfmap of a closed and bounded interval, the Mann iteration converges to a fixed point of the function. In 1974, Ishikawa [5] devised a new iteration scheme to e...

The Equivalence of Mann Iteration and Ishikawa Iteration for Non-lipschitzian Operators

We show that the convergence of Mann iteration is equivalent to the convergence of Ishikawa iteration for various classes of non-Lipschitzian operators.

Mann Iteration Converges Faster than Ishikawa Iteration for the Class of Zamfirescu Operators

On the equivalence of Mann and Ishikawa iteration methods with errors

We show that for several classes of mappings Mann and Ishikawa iteration procedures with errors in the sense of Xu [14] are equivalent. It is worth to mention here that, our results are the extensions or generalizations of some known recent results about equivalences.

Some Convergence Results for the Jungck-mann and the Jungck-ishikawa Iteration Processes in the Class of Generalized Zamfirescu Operators

In this paper, we shall establish some strong convergence results for the recently introduced Jungck-Mann iteration process of Singh et al. [18] and the newly introduced Jungck-Ishikawa iteration process in the class of non-selfmappings in an arbitrary Banach space. Our results are generalizations and extensions of those of Berinde [4], Rhoades [13, 14] as well as some other analogous ones in t...