### Abstract

Let E be a real Banach space, and let A : D (A) ⊆ E → E be a Lipschitz, ψ-expansive and accretive mapping such that over(c o, -) (D (A)) ⊆ ∩_{λ > 0} R (I + λ A). Suppose that there exists x_{0} ∈ D (A), where one of the following holds: (i) There exists R > 0 such that ψ (R) > 2 {norm of matrix} A (x_{0}) {norm of matrix}; or (ii) There exists a bounded neighborhood U of x_{0} such that t (x - x_{0}) ∉ A x for x ∈ ∂ U ∩ D (A) and t < 0. An iterative sequence {x_{n}} is constructed to converge strongly to a zero of A. Related results deal with the strong convergence of this iteration process to fixed points of ψ-expansive and pseudocontractive mappings in real Banach spaces. The convergence results established in this paper are new for this more general class of ψ-expansive and accretive or pseudocontractive mappings.

Original language | English |
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Pages (from-to) | 73-82 |

Number of pages | 10 |

Journal | Nonlinear Analysis, Theory, Methods and Applications |

Volume | 66 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 1 2007 |

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### All Science Journal Classification (ASJC) codes

- Analysis
- Applied Mathematics

### Cite this

*Nonlinear Analysis, Theory, Methods and Applications*,

*66*(1), 73-82. https://doi.org/10.1016/j.na.2005.11.011