### Abstract

Let K be a nonempty closed and convex subset of a real Banach space E. Let T : K → E be a nonexpansive weakly inward mapping with F (T) ≠ ∅ and f : K → K be a contraction. Then for t ∈ (0, 1), there exists a sequence {y_{t}} ⊂ K satisfying y_{t} = (1 - t) f (y_{t}) + tT (y_{t}). Furthermore, if E is a strictly convex real reflexive Banach space having a uniformly Gâteaux differentiable norm, then {y_{t}} converges strongly to a fixed point p of T such that p is the unique solution in F (T) to a certain variational inequality. Moreover, if {T_{i}, i = 1, 2, ..., r} is a family of nonexpansive mappings, then an explicit iteration process which converges strongly to a common fixed point of {T_{i}, i = 1, 2, ..., r} and to a solution of a certain variational inequality is constructed. Under the above setting, the family T_{i}, i = 1, 2, ..., r need not satisfy the requirment that {Mathematical expression}.

Original language | English |
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Pages (from-to) | 155-163 |

Number of pages | 9 |

Journal | Applied Mathematics and Computation |

Volume | 191 |

Issue number | 1 |

DOIs | |

Publication status | Published - Aug 1 2007 |

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### All Science Journal Classification (ASJC) codes

- Computational Mathematics
- Applied Mathematics