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Open AccessJournal ArticleDOI

Iterative Sequences for Asymptotically Quasi-nonexpansive Mappings

Liu Qihou
- 01 Jul 2001 - 
- Vol. 259, Iss: 1, pp 1-7
TLDR
Ghosh and Debnath as mentioned in this paper proved sufficient and necessary conditions for Ishikawa iterative sequences of asymptotically quasi-nonexpansive mappings to converge to fixed points.
About: 
This article is published in Journal of Mathematical Analysis and Applications.The article was published on 2001-07-01 and is currently open access. It has received 159 citations till now. The article focuses on the topics: Iterative method & Banach space.

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Citations
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Journal ArticleDOI

Iterative Sequences for Asymptotically Quasi-nonexpansive Mappings with Error Member☆

Liu Qihou
- 01 Jul 2001 - 
Journal ArticleDOI

Convergence of iterates with errors of asymptotically quasi-nonexpansive mappings and applications

Hafiz Fukhar-ud-din, +1 more
- 15 Apr 2007 - 
TL;DR: In this article, a generalized iterative process with errors is considered to approximate the common fixed points of two asymptotically quasi-none-expansive mappings, and a convergence theorem has been obtained which generalizes a known result.
Journal ArticleDOI

Strong convergence of a general iteration scheme in CAT(0) spaces

Abdul Rahim Khan, +3 more
- 01 Feb 2011 - 
TL;DR: In this paper, strong convergence of a general iteration scheme for a finite family of asymptotically quasi-nonexpansive maps in convex metric spaces and C A T ( 0 ) spaces was studied.
Journal ArticleDOI

Approximate fixed point sequences and convergence theorems for Lipschitz pseudocontractive maps

Charles E. Chidume, +1 more
TL;DR: In this article, a nonempty closed convex subset of a real Banach space is constructed for which ∥x n - Tx n ∥ → 0 as n → oc.
Journal ArticleDOI

Asymptotically nonexpansive mappings in uniformly convex hyperbolic spaces

Ulrich Kohlenbach, +1 more
- 01 Jan 2010 - 
TL;DR: In this article, a fixed point theorem for asymptotically nonexpansive mappings in uniformly convex hyperbolic spaces is provided, as well as new effective results on the Krasnosel-skii-mann iterations of such mappings.
References
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Journal ArticleDOI

Fixed point iteration processes for asymptotically nonexpansive mappings

Kok-Keong Tan, +1 more
TL;DR: In this article, the modified Mann and Ishikawa iteration processes defined by xn+, = tnTnxn+I-tn)xn and xn+ i = tNTn(snTnexn+snI-sn)xN) +(-tn) xn 7 respectively, converge weakly to a fixed point of T.
Journal ArticleDOI

Strong and weak convergence of the sequence of successive approximations for quasi-nonexpansive mappings

W.V Petryshyn, +1 more
- 01 Aug 1973 - 
TL;DR: In this article, the authors obtained conditions on T, D, and X which would guarantee the strong convergence and weak convergence of the iterates to a fixed point of T in D and X in X, respectively.
Journal ArticleDOI

Existence and convergence for fixed points of mappings of asymptotically nonexpansive type

Hong-Kun Xu
- 01 Jun 1991 - 
Journal ArticleDOI

Convergence of Ishikawa Iterates of Quasi-Nonexpansive Mappings

M. K. Ghosh, +1 more
- 01 Mar 1997 - 
TL;DR: In this paper, a necessary and sufficient condition for the convergence of Ishikawa iterates of quasi-none-expansive mapping in a Banach space is discussed, and a convergence condition for nonexpansive mappings in a uniformly convex space is also discussed.