... 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...
... 226–240.
[5] , Strong convergence of a proximal-type algorithm in a Banach space,SIAMJ.Optim.13
(2002), no. 3, 938–945.
[6] W. A. Kirk and B. Sims, Convergence of Picard iterates of nonexpansive ... beaBanachspacewithnorm
· and let E
∗
be the dual of E. Then we denote by
x, x
∗
the pairing between x ∈ E and x
∗
∈ E
∗
.When{x
n
} is a sequence in E, we denote
the stro...
... {x
n
} converges strongly to
a common fixed point of T and U.
Let C be a closed convex subset of a Banach space E and let ={T(t):t ∈ [0,∞)}
be a family of nonexpansive mappings of C into itself. ... converges strongly to a fixed point of T.
346 Weak and strong convergence theorems
a nonexpansive semigroup of C. We consider the follow i ng iterative procedure (see [...
... Strong convergence of an implicit iteration process for a finite family of nonexpansive
mappings. Nonlinear Anal. 65, 1149–1156 (2005)
7. Fukhar-ud-din, H, Khan, SH: Convergence of iterates with ... properties and applications. Theory and
Applications of Nonlinear Operators of Accretive and Monotone Type. pp. 15–50.Dekker, New York (1996)
15. Kamimura, S, Takahas...
... Banach space and let E* b e the dual space of E. For a
sequence {x
n
}ofE and a point x Î E, the weak convergence of {x
n
}tox and the strong
convergence of {x
n
}tox are denoted by x
n
⇀ x and x
n
® ... Strong convergence of an implicit iteration process for a finite family of nonexpansive
mappings. Nonlinear Anal. 65, 1149–1156 (2005)
7. Fukhar-ud-din, H, K...
... purpose of this paper is to establish a strong convergence theorem for common
fixed points of the multistep iterative scheme with errors for asymptotically nonexpansive
mappings in the intermediate ... establish strong convergence theorem for multi-step iterative scheme with errors for
asymptotically nonexpansive mappings in the intermediate sense in Banach spaces. Our...
... Our results extend and improve the recent results
of Nakajo and Takahashi 2003 and of Zegeye and Shahzad 2008 from the class of nonexpansive
mappings to asymptotically nonexpansive mappings.
1. ... method, and to prove strong convergence theorems.
In 2008, Takahashi et al. 7 proved strong convergence theorems by the new hybrid
methods for a family of non...
... element of the set of solutions of an
infinite family of equilibrium problems and the set of fixed points of a finite family of nonexpansive
mappings in a Hilbert space. We prove some strong convergence ... for finding a common element of the set of a finite family of
nonexpansive mappings and the set of solutions of an equilibrium problem, by combining
th...
... element of the set of
fixed points of hemirelatively nonexpansive mappings and the set of solutions of an equilibrium
problem and for finding a common element of the set of zero points of maximal ... element of the set of solutions of an equilibrium problem and the
set of fixed points of a hemirelatively nonexpansive mapping and for finding a common
element...
... Article
Strong Convergence of Monotone
Hybrid Method for Maximal Monotone Operators
and Hemirelatively Nonexpansive Mappings
Chakkrid Klin-eam and Suthep Suantai
Department of Mathematics, Faculty of ... problem of
finding a common element of the fixed point of nonlinear mappings and the set of solutions
of a variational inequality in the framework of Hilbert space...