### 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 |

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### All Science Journal Classification (ASJC) codes

- Modelling and Simulation
- Computer Science Applications

### Cite this

*Mathematical and Computer Modelling*,

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

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*Mathematical and Computer Modelling*, vol. 54, no. 9-10, pp. 2077-2086. https://doi.org/10.1016/j.mcm.2011.05.016

**Strong convergence theorems for a semigroup of asymptotically nonexpansive mappings.** / Zegeye, H.; Shahzad, N.; Daman, O. A.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Strong convergence theorems for a semigroup of asymptotically nonexpansive mappings

AU - Zegeye, H.

AU - Shahzad, N.

AU - Daman, O. A.

PY - 2011/11/1

Y1 - 2011/11/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=80051664379&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=80051664379&partnerID=8YFLogxK

U2 - 10.1016/j.mcm.2011.05.016

DO - 10.1016/j.mcm.2011.05.016

M3 - Article

AN - SCOPUS:80051664379

VL - 54

SP - 2077

EP - 2086

JO - Mathematical and Computer Modelling

JF - Mathematical and Computer Modelling

SN - 0895-7177

IS - 9-10

ER -