... 2011:96
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RESEARC H Open Access
Weak and strong convergence theorems of
implicit iteration process on Banach spaces
Lai-Jiu Lin
1*
, ... Lin et al.: Weak and strong convergence theorems of implicit iteration process on Banach
spaces. Fixed Point Theory and Applications...
... consider weak convergence theorems of implicit iterative
processes for two nonexpansive mappings and a mapping which satisfies condition (C).
Next, we consider strong convergence theorem of an implicit- shrinking ... iterative process
for two nonexpansive mappings and a relative nonexpansive mapping on Banach
spaces. Note that the conditions of strong convergen...
... article as: Li and Jiang: Maximal and minimal point theorems and Caristi’s fixed point theorem. Fixed
Point Theory and Applications 2011 2011:103.
Li and Jiang Fixed Point Theory and Applications ... existence theorems of maximal
and minimal points are established. By using them, some generalized Caristi’s fixed
point theorems are proved, whic...
... H.
Inspired by Bauschke and Combettes 1 and Takahashi et al. 4, we present a
shrinking projection method for the class of T mappings. Furthermore, we obtain a shrinking
projection method for a ... Point Theory and Applications
Combettes 2, Bauschke, and Combettes 1 studied properties of the class T
mappings and presented several algorithms. They introduced an abs...
... G. Cai and C. S. Hu, Strong convergence theorems of a general iterative process for a finite family
of λ
i
-strict pseudo -contractions in q-uniformly smooth Banach spaces,” Computers & Mathematics ... 0.
Fixed Point Theory and Applications 19
9 X. Qin and Y. Su, “Approximation of a zero point of accretive operator in Banach spaces,” Journal...
... Viscosity
Iterative Methods for a Countable Family of Strict
Pseudo-contractions in Banach Spaces
Rabian Wangkeeree and Uthai Kamraksa
Department of Mathematics, Faculty of Science, Naresuan University, ... Kimura, W. Takahashi, and M. Toyoda, “Approximation of common fixed points of a
countable family of nonexpansive mappings in a Banach space,” N...
... establish strong convergence theorems of
the modified Mann iteration scheme to λ -strict pseudocontractions in p -uniformly convex Banach
spaces with a uniformly G
ˆ
ateaux differentiable norm. The main ... in
the following four aspects: 1 in contrast to weak convergence results in 2–4 ,strong
convergence theorems of the modified Mann iterative sequence are obt...
... some strong convergence theorems for fixed points of modified Ishikawa and Halpern
iterative processes for a countable family of hemi-relatively nonexpansive mappings in a uniformly
convex and uniformly ... and Applications
Volume 2009, Article ID 483497, 25 pages
doi:10.1155/2009/483497
Research Article
Strong Convergence Theorems of Modified
Ishikawa Iterat...
... Applications
Volume 2009, Article ID 962303, 7 pages
doi:10.1155/2009/962303
Research Article
Strong Convergence Theorems for In nitely
Nonexpansive Mappings in Hilbert Space
Yi-An Chen
College of ... Anthony To Ming Lau
We introduce a modified Ishikawa iterative process for approximating a fixed point of two
in nitely nonexpansive self -mappings by using the...
... W. Takahashi, Y. Takeuchi, and R. Kubota, Strong convergence theorems by hybrid methods
for families of nonexpansive mappings in Hilbert spaces,” Journal of Mathematical Analysis and
Applications, ... “On a hybrid method for a family of relatively nonexpansive mappings
in a Banach space,” Journal of Mathematical Analysis and Applications, vol. 357, no. 2, pp. 356–363,...
... Applications
Volume 2008, Article ID 745010, 7 pages
doi:10.1155/2008/745010
Research Article
Strong Convergence Theorems for Nonexpansive
Semigroups without Bochner Integrals
Satit Saejung
Department ... Chen, Strong convergence theorems of the CQ method for nonexpansive semigroups, ”
Fixed Point Theory and Applications, vol. 2007, Article ID 59735, 8 page...
... show strong convergence theorems of the CQ method for
nonexpansive semigroups in Hilbert spaces by hybrid method in the mathematical
programming. The results presented extend and improve the corresponding ... Applications
Volume 2007, Article ID 59735, 8 pages
doi:10.1155/2007/59735
Research Article
Strong Convergence Theorems of the CQ Method...
... convergence
theorems of the multistep iterative scheme with errors for a finite family of nonexpansive
nonself-mappings. More precisely, we prove weak convergence of these implicit iteration
WEAK AND STRONG CONVERGENCE ... with the study of a multistep iterative scheme with errors involving
a finite family of nonexpansive nonself-mappings. We approximate th...
... introduce an iterative sequence for finding fixed points of relatively nonexpansive
mappings in Banach spaces, and then prove weak and strong convergence theorems by
using the notion of generalized ... V
p,x
n+1
,
(3.25)
WEAK AND STRONG CONVERGENCE THEOREMS
FOR RELATIVELY NONEXPANSIVE MAPPINGS
IN BANACH SPACES
SHIN-YA MATSUSHITA AND WATARU TA...
... CONVERGENCE THEOREMS FOR
NONEXPANSIVE SEMIGROUPS IN BANACH SPACES
SACHIKO ATSUSHIBA AND WATARU TAKAHASHI
Received 24 February 2005
We introduce an implicit iterative process for a nonexpansive ... Strong convergence theorems for finite quasi -nonexpansive mappings, Comm. Appl.
Nonlinear Anal. 9 (2002), no. 3, 57–68.
[2] , Strong convergence theorems...