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

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

Picard Iteration Converges Faster than Mann Iteration for a Class of Quasi-contractive Operators

In the last three decades many papers have been published on the iterative approximation of fixed points for certain classes of operators, using the Mann and Ishikawa iteration methods, see [4], for a recent survey. These papers were motivated by the fact that, under weaker contractive type conditions, the Picard iteration (or the method of successive approximations), need not converge to the f...

Picard iteration converges faster than Mann iteration for a class of quasi-contractive operators

The purpose of this paper is to introduce a new class of quasi-contractive operators and to show that the most used fixed point iterative methods, that is, the Picard and Mann iterations, are convergent to the unique fixed point. The comparison of these methods with respect to their convergence rate is obtained.

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...

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.