In this paper, we define and study convergence of an Ishikawa type iteration scheme with a new and weaker control condition for two nonself asymptotically quasi-nonexpansive mappings on a uniformly convex Banach space.

In this paper, we discuss the convergence of random Ishikawa iteration scheme to a common random fixed point for a certain class of random operators in Banach spaces. AMS Mathematics Subject Classification (2010): 47H10, 54H25

In this paper, we prove the existence of a random common fixed point of two continuous contractive random operators on a separable Banach space. We introduce the random modified Ishikawa iteration scheme and use our existence result to study weak and strong convergence of this scheme to a unique random common fixed point of two random asymptotically quasi-nonexpansive operator. Our work extends...

* Correspondence: [email protected] Department of Mathematics, Ataturk University, Erzurum 25240, Turkey Full list of author information is available at the end of the article Abstract In this article, we first give a multivalued version of an iteration scheme of Agarwal et al. We use an idea due to Shahzad and Zegeye which removes a “strong condition” on the mapping involved in the ite...

In this paper, we introduce a modified Ishikawa iterative process for approximating a fixed point of nonexpansive mappings in Hilbert spaces. we establish the strong convergence theorem of the general iteration scheme under some mild conditions. Our results extend and improve the results announced by many others.

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.

In this paper, by means of the concept of attractive points of a nonlinear mapping, we prove strong convergence theorem of the Ishikawa iteration for an (α, β)−generalized hybrid mapping in a uniformly convex Banach space, and obtain weak convergence theorem of the Ishikawa iteration for such a mapping in a Hilbert space.

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 ...

The stability of iterative procedures plays an important role while solving the nonlinear equations obtained out of a physical problem using the advanced computational tools. The main purpose of this paper is to present a weaker stability result for Jungck-Ishikawa iteration process for a map satisfying some general contractive conditions in metric spaces. Some well known recent results are als...

This paper introduce a iteration scheme for approximation of strongly accretive operator equations in reflexive Banach space with weakly continuous duality mapping. Our result improve the results of Y. Xu [Ishikawa and Mann Iterative Processes with Errors for Nonlinear Strongly Accretive Operator Equations, J. Math. Anal Appl. 224(1998) 91-101] and I. Inchan and S. Plubtieng [Approximating solu...