### Abstract

Let K be a nonempty closed convex and bounded subset of a real Banach space E. Let T ℑ: ={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 μ_{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,∈ Ndbl; atisfying||u_{n}-T (t)u_{n}||→0 as→n ∞, for any t+, where [image omitted]. If, in addition, E is uniformly convex with uniformly G[image omitted]teaux differentiable norm, then it is proved that F(ℑ) ≠ ∅ and the sequence {u_{n}} converges strongly to a point of F(ℑ) under certain mild conditions on {L_{t}}, {t _{n}} and {s_{n}}. Moreover, it is proved that an explicit sequence {x_{n}} generated from x1 ∈ K by x_{n}+1: α _{n}u_{0}+(1-α_{n}n)T(t_{n})x _{n}, n ≥1,converges to a fixed point of T under appropriate assumption imposed upon the sequence {x_{n}}.

Original language | English |
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Pages (from-to) | 833-848 |

Number of pages | 16 |

Journal | Numerical Functional Analysis and Optimization |

Volume | 30 |

Issue number | 7-8 |

DOIs | |

Publication status | Published - Jul 1 2009 |

### All Science Journal Classification (ASJC) codes

- Analysis
- Signal Processing
- Computer Science Applications
- Control and Optimization