### 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 |

### All Science Journal Classification (ASJC) codes

- Geometry and Topology
- Applied Mathematics

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## Cite this

Chidume, C. E., Zegeye, H., & Shahzad, N. (2005). Convergence theorems for a common fixed point of a finite family of nonself nonexpansive mappings.

*Fixed Point Theory and Applications*,*2005*(2), 233-241. https://doi.org/10.1155/FPTA.2005.233