Abstract
Let
K
be a nonempty closed convex subset of a real Banach space
E
. Let
T
:
=
{
T
(
t
)
:
t
≥
0
}
be a strongly continuous semigroup of asymptotically nonexpansive mappings from
K
into
K
with a sequence
{
L
t
}
⊂
[
1
,
∞
)
. Suppose
F
(
T
)
≠
0̸
. Then, for a given
u
∈
K
there exists a sequence
{
u
n
}
⊂
K
such that
u
n
=
(
1
−
α
n
)
1
t
n
∫
0
t
n
T
(
s
)
u
n
d
s
+
α
n
u
, for
n
∈
N
, where
t
n
∈
R
+
,
{
α
n
}
⊂
(
0
,
1
)
and
{
L
t
}
satisfy certain conditions. Suppose, in addition, that
E
is reflexive strictly convex with a Gâteaux differentiable norm. Then, the sequence
{
u
n
}
converges strongly to a point of
F
(
T
)
. Furthermore, an
explicit sequence
{
x
n
}
which converges strongly to a fixed point of
T
is proved.