### Abstract

Let K be a nonempty closed convex subset of a uniformly convex real Banach space E which has uniformly Gâteaux differentiable norm. Let (Formula presented.) be a strongly continuous uniformly L-Lipschitzian semi-group of pseudocontractive mappings from K into E satisfying the weakly inward condition with a nonempty common fixed point set. Then, for a given u∈K, there exists a unique point u _{n} in K satisfying (Formula presented.), where α _{n} ∈[0,1) and t _{n} > 0 are real sequences satisfying appropriate conditions. Furthermore, {u _{n} } converges strongly to a fixed point of (Formula presented.). Moreover, explicit iteration procedures which converge strongly to a fixed point of (Formula presented.) are constructed. A corollary of this result gives an affirmative answer to a recent question posed in Suzuki (2003, Proceedings of the American Mathematical Society, 131, 2133–2136).

Original language | English |
---|---|

Pages (from-to) | 353-366 |

Number of pages | 14 |

Journal | Applicable Analysis |

Volume | 86 |

Issue number | 3 |

DOIs | |

Publication status | Published - Mar 2007 |

### All Science Journal Classification (ASJC) codes

- Analysis
- Applied Mathematics