### 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 {Lt}∪[1,∞). Suppose F(T)≠Ø. Then, for a given uεK there exists a sequence {un}∪K such that un=(1-αn)1tn∫0tnT(s)unds+αnu, for nεN, where tnεR+, {αn}∪(0,1) and {Lt} satisfy certain conditions. Suppose, in addition, that E is reflexive strictly convex with a Gâteaux differentiable norm. Then, the sequence {un} converges strongly to a point of F(T). Furthermore, an explicit sequence {xn} which converges strongly to a fixed point of T is proved.

Original language | English |
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Pages (from-to) | 2077-2086 |

Number of pages | 10 |

Journal | Mathematical and Computer Modelling |

Volume | 54 |

Issue number | 9-10 |

DOIs | |

Publication status | Published - Nov 1 2011 |

### All Science Journal Classification (ASJC) codes

- Modelling and Simulation
- Computer Science Applications

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## Cite this

Zegeye, H., Shahzad, N., & Daman, O. A. (2011). Strong convergence theorems for a semigroup of asymptotically nonexpansive mappings.

*Mathematical and Computer Modelling*,*54*(9-10), 2077-2086. https://doi.org/10.1016/j.mcm.2011.05.016