In this paper, several weak and strong convergence theorems are established for a new modified iterations with errors for finite family of nonself asymptotically nonexpansive mappings in Banach spaces. Mann-type, Ishikawa-type and Noor-type iterations are covered by the new iteration scheme. Our convergence theorems improve, unify and generalize many important results in the current literatures.

We introduce a modified Noor iteration scheme generated by an infinite family of strict pseudo-contractive mappings and prove the strong convergence theorems of the scheme in the framework of q−uniformly smooth and strictly convex Banach space. Results shown here are extensions and refinements of previously known results.

In this paper, we prove the weak convergence of a modified Khan iteration for nonself I nonexpansive mapping in a Banach space which satisfies Opial’s condition. Our result extends and improves these announced by S. Chornphrom and S.Phonin [Weak Converges Theorem of Noor iterative Scheme for Nonself I-Nonexpansive mapping, Thai Journal of Mathematics Volume 7(2009) no.2:311-317].

We prove a strong convergence theorem for the modified Noor iterations‎ ‎in the framework of CAT(0) spaces‎. ‎Our results extend and improve the corresponding results of‎ ‎X‎. ‎Qin‎, ‎Y‎. ‎Su and M‎. ‎Shang‎, ‎T‎. ‎H‎. ‎Kim and H‎. ‎K‎. ‎Xu and S‎. ‎Saejung‎ ‎and some others‎.

we prove a strong convergence theorem for the modified noor iterations‎ ‎in the framework of cat(0) spaces‎. ‎our results extend and improve the corresponding results of‎ ‎x‎. ‎qin‎, ‎y‎. ‎su and m‎. ‎shang‎, ‎t‎. ‎h‎. ‎kim and h‎. ‎k‎. ‎xu and s‎. ‎saejung‎ ‎and some others‎.

Let T be a local strongly pseudocontractive and uniformly continuous operator from an arbitrary Banach space X into itself. Under certain conditions, we establish that the Noor iteration scheme with errors both converges strongly to a unique fixed point of T and is almost T -stable. The related results deal with the convergence and almost stability of the Noor iteration scheme with errors of so...

In a recent paper, Noor and Noor [K. Inayat Noor, M. Aslam Noor, Predictor–corrector Halley method for nonlinear equations, Appl. Math. Comput., in press, doi:10.1016/j.amc.11.023] have suggested and analyzed a predictor–corrector method Halley method for solving nonlinear equations. In this paper, we modified this method by using the finite difference scheme, which has a quintic convergence. W...

In this note, we give fixed point results in fractal generation (Julia sets and Mandelbrot sets) by using Noor iteration scheme with s-convexity. Researchers have already presented fixed point results in Mann and Ishikawa orbits that are examples of one-step and two-step feedback processes respectively. In this paper we present fixed point results in Noor orbit, which is a three-step iterative ...

In this paper, we obtained the convergence of modified Noor iterative scheme for nearly Lipschitzian maps in real Banach spaces. Our results contribute to the literature in this area of re- search.