... 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...
... many results not cited here.
On the other hand, in the last twenty years or so, there are many papers in the
literature dealing with the iteration approximating fixed points of Lipschitz strongly ... 15 obtained strong convergence theorems on a mixed iteration
scheme by the viscosity approximation methods for λ-strict pseudo-contractions in p-
uniformly convex Banach spaces with...
... operator with
coefficient
γ>0. Assume that 0 <γ<γ. Then the sequence {x
t
} define by x
t
t φx
t
1 −tATx
t
converges strongly as t → 0 to a fixed point x of T which solves the variational ... bounded.
To prove that x
t
→ x x ∈ F T as t → 0.
Since {x
t
} is bounded and E is reflexive, there exists a subsequence {x
t
n
} of {x
t
} such
that x
t
n
x...
... different with ones of others.
4. Applications for Multiobjective Optimization Problem
In this section, we study a kind of multiobjective optimization problem by using the result
of this paper. That ... point of T. The
set of fixed points of T is denoted by F T . It is well known that F T is closed convex and
also nonempty if T has a bounded trajectory see 1.
2 Fixed Point Theory...
... Theorem 4.1 that the net {x
t
}
generated by x
t
tfx
t
1 − t T
δ
x
t
converges strongly to q ∈ Fix T
δ
Fix T ,ast → 0.
Clearly,
x
t
− y
n
1 − t
T
δ
x
t
− y
n
t
f
x
t
− y
n
. ... Point Theory and Applications
for all x, y ∈ C. We note that the class of λ-strict pseudocontractions strictly includes the class
of nonexpansive mappings wh...
... Wang, and J C. Yao, Strong convergence theorems by a relaxed extragradient
method for a general system of variational inequalities,” Mathematical Methods of Operations Research,
vol. 67, no. ... retraction of C if there exists a sunny
nonexpansive retraction from C onto D.ItiswellknownthatifX is a Hilbert space, then a
sunny nonexpansive retraction Q
C
is coincident with the metr...
... maps {T
i
: i ∈ I} and or the
parameters {α
n
} are sufficient to guarantee strong convergence of the sequence in Theorem
XO?
The aim of this paper is to study strong convergence of iterative ... recent results from the current literature.
1. Introduction
A metric space X, d is said to be a length space if any two points of X are joined by a rectifiable
path i.e., a path of finite...
... Ansari
Copyright q 2011 A. Cuntavepanit and B. Panyanak. This is an open access article distributed
under the Creative Commons Attribution License, which permits unrestricted use, distribution,
and ... “An iterative approach to quadratic optimization,” Journal of Optimization Theory and
Applications, vol. 116, no. 3, pp. 659–678, 2003.
11 H K. Xu, “A strong convergence theorem for c...
... literature. See, for example, 2–8.
In 1997, Combettes and Hirstoaga 9 introduced an iterative method for finding
the best approximation to the initial data and proved a strong convergence theorem.
Subsequently, ... P
∩
∞
n1
F T
n
∩VIA,C∩EPΘ
fx
∗
.
By Theorem 3.1, we obtain some interesting strong convergence theorems.
Setting T
n
x x then we have W
n
x x in T...
... to thank professor Somyot Plubtieng for drawing my attention to
the subject and for many useful discussions and the referees for helpful suggestions that
improved the contents of the paper. This ... function L : 0, ∞ → 0, ∞ such that, for each
t& gt;0, T t x − T t y≤L
t
x − y, for all x, y ∈ C.
A Lipschitzian semigroup T is called nonexpansive if L
t
1 for all t&...