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Implicit Iteration Methods with Errors for Discrete Non-Lipschitzian Families with Perturbed Mappings
Kim Tae-Hwa,Kim Kui-Yeon
Journal of Inequalities and Applications , 2010,
Abstract: Motivated and inspired by the recent works on implicit iteration methods, we prove necessary and sufficient conditions for strong convergence of the eventually implicit iteration methods with errors to a common fixed point of a discrete family which is continuous total asymptotically nonexpansive (in brief, TAN) on -uniformly smooth Banach spaces with a perturbed mapping , , under some suitable control conditions of parameters. Some applications to viscosity approximation methods or to the eventually implicit algorithms with errors for a finite family of TAN self-mappings in real Banach spaces are also added.
Implicit Iteration Methods with Errors for Discrete Non-Lipschitzian Families with Perturbed Mappings  [cached]
Tae-Hwa Kim,Kui-Yeon Kim
Journal of Inequalities and Applications , 2010, DOI: 10.1155/2010/820535
Abstract: Motivated and inspired by the recent works on implicit iteration methods, we prove necessary and sufficient conditions for strong convergence of the eventually implicit iteration methods with errors to a common fixed point of a discrete family which is continuous total asymptotically nonexpansive (in brief, TAN) on q-uniformly smooth Banach spaces with a perturbed mapping F, 1
CONVERGENCE OF IMPLICIT ITERATIVE PROCESS WITH ERRORS FOR A FINITE FAMILY OF ASYMPTOTICALLY NONEXPANSIVE MAPPINGS
Gu Feng,
谷峰

数学物理学报(A辑) , 2006,
Abstract: The purpose of this article is to study the weak and strong convergence of implicit iteration process with errors to a common fixed point for a finite family of asymptotically nonexpansive mappings and nonexpansive mappings in Banach spaces. The results presented in this article extend and improve thecorresponding results of 1, 2, 4-9, 11-15].
Convergence of implicit iterates with errors for mappings with unbounded domain in Banach spaces
Hafiz Fukhar-Ud-Din,Abdul Rahim Khan
International Journal of Mathematics and Mathematical Sciences , 2005, DOI: 10.1155/ijmms.2005.1643
Abstract: We prove that an implicit iterative process with errors converges weakly and strongly to a common fixed point of a finite family of asymptotically quasi-nonexpansive mappings on unbounded sets in a uniformly convex Banach space. Our results generalize and improve upon, among others, the corresponding recent results of Sun (2003) in the following two different directions: (i) domain of the mappings is unbounded, (ii) the iterative sequence contains an error term.
Convergence Theorems of an Implicit Iterates with Errors for Total Asymptotically Pseudo-Contractive Mappings
G.S. Saluja
International Journal of Analysis and Applications , 2013,
Abstract: The goal of this paper is to establish weak and strong convergence theorems of an implicit iteration process with errors to converge to common fixed points for a finite family of uniformly $L$-Lipschitzian total asymptotically pseudo-contractive mappings in the framework of Banach spaces. Our results extend the corresponding result of [2.5.8.10] and many others.
Weak and Strong Convergence of an Implicit Iteration Process for an Asymptotically Quasi- -Nonexpansive Mapping in Banach Space  [cached]
Mukhamedov Farrukh,Saburov Mansoor
Fixed Point Theory and Applications , 2010,
Abstract: We prove the weak and strong convergence of the implicit iterative process to a common fixed point of an asymptotically quasi- -nonexpansive mapping and an asymptotically quasi-nonexpansive mapping , defined on a nonempty closed convex subset of a Banach space.
Weak and Strong Convergence of an Implicit Iteration Process for an Asymptotically Quasi-I-Nonexpansive Mapping in Banach Space  [cached]
Farrukh Mukhamedov,Mansoor Saburov
Fixed Point Theory and Applications , 2010, DOI: 10.1155/2010/719631
Abstract: We prove the weak and strong convergence of the implicit iterative process to a common fixed point of an asymptotically quasi-I-nonexpansive mapping T and an asymptotically quasi-nonexpansive mapping I, defined on a nonempty closed convex subset of a Banach space.
Weak and strong convergence of an implicit iterative process with errors for a finite family of asymptotically quasi $I-$nonexpansive mappings in Banach space  [PDF]
Farrukh Mukhamedov,Mansoor Saburov
Mathematics , 2010,
Abstract: In this paper we prove the weak and strong convergence of the implicit iterative process with errors to a common fixed point of a finite family $\{T_j\}_{i=1}^N$ of asymptotically quasi $I_j-$nonexpansive mappings as well as a family of $\{I_j\}_{j=1}^N$ of asymptotically quasi nonexpansive mappings in the framework of Banach spaces.
A new composite implicit iterative process for a finite family of nonexpansive mappings in Banach spaces  [cached]
Feng Gu,Jing Lu
Fixed Point Theory and Applications , 2006, DOI: 10.1155/fpta/2006/82738
Abstract: The purpose of this paper is to study the weak and strong convergence of implicit iteration process with errors to a common fixed point for a finite family of nonexpansive mappings in Banach spaces. The results presented in this paper extend and improve the corresponding results of Chang and Cho (2003), Xu and Ori (2001), and Zhou and Chang (2002).
A new composite implicit iterative process for a finite family of nonexpansive mappings in Banach spaces  [cached]
Gu Feng,Lu Jing
Fixed Point Theory and Applications , 2006,
Abstract: The purpose of this paper is to study the weak and strong convergence of implicit iteration process with errors to a common fixed point for a finite family of nonexpansive mappings in Banach spaces. The results presented in this paper extend and improve the corresponding results of Chang and Cho (2003), Xu and Ori (2001), and Zhou and Chang (2002).
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