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Abstract
Let K be a nonempty closed convex and bounded subset of a real Banach space E. Let : = {T(t): t ∊ ℝ+} be a strongly continuous semigroup of asymptotically nonexpansive self-mappings on K with a sequence {L
t
} ⊂ [1, ∞). Then, for a given u
0 ∊ K and s
n
∊ (0, 1), t
n
> 0 there exists a sequence {u
n
} ⊂ K such that u
n
= (1 − α
n
)T(t
n
)u
n
+ α
n
u
0, for each n ∊ ℕ, satisfying | u
n
− T(t)u
n
| → 0 as n → ∞, for any t ∊ ℝ+, where . If, in addition, E is uniformly convex with uniformly G
teaux differentiable norm, then it is proved that F() ≠ and the sequence {u
n
} converges strongly to a point of F() under certain mild conditions on {L
t
}, {t
n
} and {s
n
}. Moreover, it is proved that an explicit sequence {x
n
} generated from x
1 ∊ K by x
n+1: = α
n
u
0 + (1 − α
n
)T(t
n
)x
n
, n ≥ 1, converges to a fixed point of under appropriate assumption imposed upon the sequence {x
n
}.