The purpose of this article is to prove strong convergence theorems for weak relatively nonexpansive mapping which is firstly presented in this article. In order to get the strong convergence theorems for weak relatively nonexpansive mapping, the monotone CQ iteration method is presented and is used to approximate the fixed point of weak relatively nonexpansive mapping, therefore this article a...

and Applied Analysis 3 Lemma 1.1 see 21 . let X be a uniformly convex Banach space. Let b and c be two constants with 0 < b < c < 1. Suppose that {tn} is a sequence in b, c . Let {xn} and {yn} be two sequences in X such that lim sup n→∞ ‖xn‖ ≤ d, lim sup n→∞ ∥ yn ∥ ∥ ≤ d, lim n→∞ ∥ tnxn 1 − tn yn ∥ ∥ d 1.8 hold for some d ≥ 0, then limn→∞‖xn − yn‖ 0. Lemma 1.2 see 26 . Let {an}, {bn}, and {cn} ...

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.

Combining these three definitions, Zamfirescu [12] proved the following important result. Theorem 1.1. Let (X ,d) be a complete metric space and T : X → X a mapping for which there exists the real numbers a,b, and c satisfying a∈ (0,1), b,c ∈ (0,1/2) such that for each pair x, y ∈ X , at least one of the following conditions holds: (z1) d(Tx,Ty)≤ ad(x, y), (z2) d(Tx,Ty)≤ b[d(x,Tx) +d(y,Ty)], (z...

A new general composite implicit random iteration scheme with perturbed mapping is proposed and obtain necessary and sufficient conditions for strong convergence of proposed iteration scheme to random fixed point of a finite family of random nonexpansive mappings are obtained.

In this paper, we study the Picard-Mann hybrid iteration process to approximate fixed points of Suzuki's generalized nonexpansive mappings. We establish some weak and strong convergence theorems for such mappings in uniformly convex Banach space.

In this paper, we prove the weak and strong convergence of the Ishikawa iterative scheme with errors to a common fixed point for two asymptotically nonexpansive mappings in a uniformly convex Banach space under a condition weaker than compactness. Our theorems improve and generalize recent known results in literature.

with kn ≥ 0, rn ≥ 0, kn → 1, rn → 0 n → ∞ , for each x, y ∈ C, n 0, 1, 2, . . . . If kn 1 and rn 0, 1.1 reduces to nonexpansive mapping; if rn 0, 1.1 reduces to asymptotically nonexpansive mapping; if kn 1, 1.1 reduces to asymptotically nonexpansive-type mapping. So, a generalized asymptotically nonexpansive mapping is much more general than many other mappings. Browder 1 introduced the followi...

In this paper, we consider the strong convergence of the projection type Ishikawa iteration process to a common fixed point of a finite family of nonself Ii asymptotically quasi-nonexpansive mappings. Our results of this paper improve and extend the corresponding results of Temir and Gul [10], Temir [11], and Thianwan [12].

In this paper, we introduce amodifiedMann iterative process for approximating a common fixedpoint of a finite family of strict pseudo-contractions inHilbert spaces.We establish the strong convergence theorem of the general iteration scheme under some mild conditions. Our results extend and improve the recent ones announced by many others. © 2008 Elsevier Ltd. All rights reserved.