### Abstract

Let D be an open subset of a real uniformly smooth Banach space E. Suppose T: D̄ → E is a demicontinuous pseudocontractive mapping satisfying an appropriate condition, where D̄ denotes the closure of D. Then, it is proved that (i) D̄ ⊆ ℛ (I + r (I-T)) for every r > 0; (ii) for a given y_{0} ∈ D, there exists a unique path t → y_{t} ∈ D̄, t ∈ [0, 1], satisfying y_{t} := tTy_{t} + (1-t) y_{0}. Moreover, if F (T) ≠ ∅ or there exists y_{0} ∈ D such that the set K := {y ∈ D: T y = λ y + (1-λ) y_{0} for λ >1} is bounded, then it is proved that, as t → 1-, the path {y_{t}} converges strongly to a fixed point of T. Furthermore, explicit iteration procedures with bounded error terms are proved to converge strongly to a fixed point of T.

Original language | English |
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Pages (from-to) | 67-77 |

Number of pages | 11 |

Journal | Fixed Point Theory and Applications |

Volume | 2005 |

Issue number | 1 |

DOIs | |

Publication status | Published - Dec 1 2005 |

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### All Science Journal Classification (ASJC) codes

- Geometry and Topology
- Applied Mathematics

### Cite this

*Fixed Point Theory and Applications*,

*2005*(1), 67-77. https://doi.org/10.1155/FPTA.2005.67