We denote the set of all fixed points of T by Fix(T); for more details see []. The concept of -convergence in general metric spaces was introduced by Lim []. Kirk [] has proved the existence of fixed point of nonexpansive mappings in CAT() spaces. Kirk and Panyanak [] specialized this concept to CAT() spaces and showed that many Banach space results involving weak convergence have precise...

The paper establishes some convergence theorems for Ishikawa type iteration processes associated with two and three quasi-nonexpansive mappings in a convex metric space.

We study the convergence of Ishikawa iteration process for the class of asymptotically κ-strict pseudocontractive mappings in the intermediate sense which is not necessarily Lipschitzian. Weak convergence theorem is established. We also obtain a strong convergence theorem by using hybrid projection for this iteration process. Our results improve and extend the corresponding results announced by...

Necessary and sufficient conditions for the convergence of Picard iteration to a fixed point for a continuous mapping in metric spaces are established. As application, we prove the convergence theorem of Ishikawa iteration to a fixed point for a nonexpansive mapping in Banach spaces. 2004 Elsevier Inc. All rights reserved.

We show some stability and convergence theorems of the modified Ishikawa iterative sequence with errors for a strongly successively pseudocontractive and strictly asymptotically pseudocontractive mapping in a real Banach space. Additionally, we prove that if T is a uniformly Lipschitzian strongly accretive mapping, the modified Ishikawa iteration sequence with errors converges strongly to the u...

In this paper, we show strong convergence theorems of modified Ishikawa iteration with errors and modified Halpern iteration with error for relatively nonexpansive mappings in a Banach space. The results extend and improve the corresponding results of Nakajo, Takahashi, Kim, Martinez-Yanes, Xu and some others. Mathematics Subject Classification: 47H09; 47H10

In this paper we introduce the Jungck-Agarwal et al. iteration procedure and obtain strong convergence as well as stability results for a pair of non-self mappings. The results obtained are generalization of some existing results in the literature. In addition, we show that the rate of convergence of this newly defined iteration procedure is better than JungckMann, Jungck-Ishikawa and JungckNoo...