... have
y − Px,x − Px≤0 (3.4)
for each y
∈ F(S)
F(T).
STRONG CONVERGENCE TO COMMON FIXED
POINTS OF NONEXPANSIVE MAPPINGS WITHOUT
COMMUTATIVITY ASSUMPTION
YONGHONG YAO, RUDONG CHEN, AND HAIYUN ... subset of H.A
mapping T of C into itself is said to be nonexpansive if
Tx− Ty≤x − y, (1.1)
for each x, y
∈ C.ForamappingT of C into itself, we denote by F(T) the se...
... using strongly monotone and lipschitzian operator, we introduce a
general iterative process for finding a common fixed point of a semigroup of
nonexpansive mappings, with respect to strongly left ... nonempty closed
convex subset of H.AmappingT of C into itself is called nonexpansive if || Tx - Ty
||≤|| x - y ||, for all x, y Î H.ByFix(T), we denote the set of fixed po...
... continuous semigroup of mappings
is F(T(1)) ∩F(T(
√
2)), submitted to Proc. Amer. Math. Soc.
[19] , Strong convergence theorem to common fixed points of two nonex pansive mappings in
general Banach ... Approximation of fixed points of nonexpansive mappings, Arch.Math.(Basel)58
(1992), no. 5, 486–491.
Tomonari Suzuki: Department of Mathematics, Kyushu Institute of...
... said to be a sunny nonexpansive retract of B if there exists a sunny
nonexpansive retraction P of B onto D.WeknowthatifE is smooth and P is a retraction
of B onto D, then P is sunny and nonexpansive ... convergence to fixed points of asymptotically nonexpansive mappings, ”
Bulletin of the Australian Mathematical Society, vol. 43, no. 1, pp. 153–159, 1991.
27 K K. T...
... “Approximation of common fixed points of families of
nonexpansive mappings, ” to appear in Taiwanese Journal of Mathematics.
[7] R. Wittmann, “Approximation of fixed points of nonexpansive mappings, ” ... easy to show that there exists at most one sunny nonexpansive retraction of C onto
D. If there is a sunny nonexpansive retraction of C onto D,thenD is said...
... “Strong convergence to common fixed points of families of
nonexpansive mappings in Banach spaces,” Journal of Nonlinear and Convex Analysis, vol. 8, no. 1, pp.
11–34, 2007.
10 Z. Opial, “Weak convergence ... ⊂
∞
n1
FT
n
, where FT
N
is the set of all fixed
points of T
n
and FT is the set of all common fixed points of T. We consider the following
cond...
... point of T provided that Tx = x. Denote by F(T) the set
of fixed points of T, that is, F(T)
={x ∈ C : Tx = x}. It is known that F(T)isclosedand
convex.
Construction of fixed points of nonexpansive mappings ... T
nmodN
, for common fixed points of a finite family of nonexpansive mappings
{T
i
}
N
i
=1
in Hilbert spaces and to prove strong convergence theorems.
We...
... com-
mon e lement of the set of solution of a monotone, Lipschitz-continuous variational
inequality problem and the set of common fixed points of an infinite family of
Yao et al. Fixed Point Theory ... problems and fixed point problems of infinite family
of nonexpansive mappings. Fixed Point Theory and Applications 2007, 12 (2007). Article ID 64363
32. Goebel, K...
... finding a common element of the set of
solutions of variational inequality and the set of common fixed points of a countable
family of nonexpansive mappings is introduced and studied. A strong convergence
theorem ... convergence
theorem of the proposed iterative scheme to a common fixed point of a countable
family of nonexpansive mappings and a solu...
... finding a common element of the set
of a generalized equilibrium problem of the set of solution to a system of variational
inequalities, and of the set of fixed points of an infinite family of strict ... independent of the class of -strict pseudo-contractions.
We denote by F(T) the set of fixed points of T.IfC ⊂ H is bounded, closed and con-
vex and T is...