### Abstract

Let K be a closed convex subset of a Banach space E and let T : K → E be a continuous weakly inward pseudocontractive mapping. Then for t ∈ (0, 1), there exists a sequence {y_{t}} ⊂ K satisfying y_{t} = (1 - t)f(y_{t}) + tT(y_{t}), where f ∈ Π_{K} {colon equals} {f : K → K, a contraction with a suitable contractive constant}. Suppose further that F(T) ≠ ∅ and E is reflexive and strictly convex which has uniformly Gâteaux differentiable norm. Then it is proved that {y_{t}} converges strongly to a fixed point of T which is also a solution of certain variational inequality. Moreover, an explicit iteration process which converges strongly to a fixed point of T and hence to a solution of certain variational inequality is constructed provided that T is Lipschitzian.

Original language | English |
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Pages (from-to) | 538-546 |

Number of pages | 9 |

Journal | Applied Mathematics and Computation |

Volume | 185 |

Issue number | 1 |

DOIs | |

Publication status | Published - Feb 1 2007 |

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### All Science Journal Classification (ASJC) codes

- Computational Mathematics
- Applied Mathematics

### Cite this

*Applied Mathematics and Computation*,

*185*(1), 538-546. https://doi.org/10.1016/j.amc.2006.07.063