### Abstract

Suppose K is a closed convex nonexpansive retract of a real uniformly smooth Banach space E with P as the nonexpansive retraction. Suppose T : K → E is an asymptotically d-weakly contractive map with sequence {k _{n} }, k _{n} ≥ 1, lim k _{n} = 1 and with F(T) _{n} int (K) ≠ øF(T):= {x ∈ K: Tx = x}. Suppose {x _{n} } is iteratively defined by x _{n+1} = P((l − k _{n} α _{n} )x _{n} +k _{n} α _{n} T(PT) ^{n−l} x _{n} ), n = 1,2,.., x _{1} ∈ K, where α _{n} ∈ (0, l) satisfies lim α _{n} = 0 and Σα _{n} = ∞. It is proved that {x _{n} } converges strongly to some x ^{*} ∈ F(T)∩ int K. Furthermore, if K is a closed convex subset of an arbitrary real Banach space and T is, in addition uniformly continuous, with F(T) ≠ ø, it is proved that {x _{n} } converges strongly to some x ^{*} ∈ F(T). ^{†} The author undertook this work when he was visiting the Abdus Salam International Center for Theoretical Physics, Trieste, Italy, as a postdoctoral fellow. ^{‡} Department of Mathematics, University of Nigeria, Nsukka.

Original language | English |
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Pages (from-to) | 701-712 |

Number of pages | 12 |

Journal | Applicable Analysis |

Volume | 82 |

Issue number | 7 |

DOIs | |

Publication status | Published - Jul 2003 |

### All Science Journal Classification (ASJC) codes

- Analysis
- Applied Mathematics

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## Cite this

*Applicable Analysis*,

*82*(7), 701-712. https://doi.org/10.1080/0003681031000140058