### Abstract

Let K be a nonempty closed convex subset of a reflexive real Banach space E which has a uniformly Gâteaux differentiable norm. Assume that K is a sunny nonexpansive retract of E with Q as the sunny nonexpansive retraction. Let T_{i}: K → E, i = 1,..., r, be a family of nonexpansive mappings which are weakly inward. Assume that every nonempty closed bounded convex subset of K has the fixed point property for nonexpansive mappings. A strong convergence theorem is proved for a common fixed point of a family of nonexpansive mappings provided that T_{i}, i = 1, 2,..., r, satisfy some mild conditions.

Original language | English |
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Pages (from-to) | 233-241 |

Number of pages | 9 |

Journal | Fixed Point Theory and Applications |

Volume | 2005 |

Issue number | 2 |

DOIs | |

Publication status | Published - Dec 1 2005 |

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### All Science Journal Classification (ASJC) codes

- Geometry and Topology
- Applied Mathematics

### Cite this

*Fixed Point Theory and Applications*,

*2005*(2), 233-241. https://doi.org/10.1155/FPTA.2005.233

}

*Fixed Point Theory and Applications*, vol. 2005, no. 2, pp. 233-241. https://doi.org/10.1155/FPTA.2005.233

**Convergence theorems for a common fixed point of a finite family of nonself nonexpansive mappings.** / Chidume, C. E.; Zegeye, Habtu; Shahzad, Naseer.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Convergence theorems for a common fixed point of a finite family of nonself nonexpansive mappings

AU - Chidume, C. E.

AU - Zegeye, Habtu

AU - Shahzad, Naseer

PY - 2005/12/1

Y1 - 2005/12/1

N2 - Let K be a nonempty closed convex subset of a reflexive real Banach space E which has a uniformly Gâteaux differentiable norm. Assume that K is a sunny nonexpansive retract of E with Q as the sunny nonexpansive retraction. Let Ti: K → E, i = 1,..., r, be a family of nonexpansive mappings which are weakly inward. Assume that every nonempty closed bounded convex subset of K has the fixed point property for nonexpansive mappings. A strong convergence theorem is proved for a common fixed point of a family of nonexpansive mappings provided that Ti, i = 1, 2,..., r, satisfy some mild conditions.

AB - Let K be a nonempty closed convex subset of a reflexive real Banach space E which has a uniformly Gâteaux differentiable norm. Assume that K is a sunny nonexpansive retract of E with Q as the sunny nonexpansive retraction. Let Ti: K → E, i = 1,..., r, be a family of nonexpansive mappings which are weakly inward. Assume that every nonempty closed bounded convex subset of K has the fixed point property for nonexpansive mappings. A strong convergence theorem is proved for a common fixed point of a family of nonexpansive mappings provided that Ti, i = 1, 2,..., r, satisfy some mild conditions.

UR - http://www.scopus.com/inward/record.url?scp=33749552101&partnerID=8YFLogxK

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U2 - 10.1155/FPTA.2005.233

DO - 10.1155/FPTA.2005.233

M3 - Article

VL - 2005

SP - 233

EP - 241

JO - Fixed Point Theory and Applications

JF - Fixed Point Theory and Applications

SN - 1687-1820

IS - 2

ER -