### Abstract

Let E be a real q-uniformly smooth Banach space and A:E→2^{E} be an m-accretive operator which satisfies a linear growth condition of the form Ax≤c(1+x) for some constant c0 and for all x∈E. It is proved that if two real sequences {λ_{n}} and {θ_{n}} satisfy appropriate conditions, the sequence {x_{n}} generated from arbitrary x_{0}∈E by x_{n+1}=x_{n}-λ_{n}(u_{n}+θ _{n}(x_{n}-z)); u_{n}∈Ax_{n}n≥0, converges strongly to some x*∈A^{-1}(0). Furthermore, if E is a reflexive Banach space with a uniformly Gâteaux differentiable norm, and if every weakly compact convex subset of E has the fixed-point property for nonexpansive mappings and A:D(A)E→2^{E} is m-accretive, then for arbitrary, z,x_{0}∈E the sequence {x_{n}} defined by x_{n+1}+λ_{n}(u_{n+1}+θ_{n}(x _{n+1}-z))=x_{n}+e_{n}, for u_{n}∈Ax_{n}, where e_{n}∈E is such that ∑e_{n}<∞∀n≥0, converges strongly to some x*∈A^{-1}(0).

Original language | English |
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Pages (from-to) | 364-377 |

Number of pages | 14 |

Journal | Journal of Mathematical Analysis and Applications |

Volume | 257 |

Issue number | 2 |

DOIs | |

Publication status | Published - May 15 2001 |

### All Science Journal Classification (ASJC) codes

- Analysis
- Applied Mathematics

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## Cite this

*Journal of Mathematical Analysis and Applications*,

*257*(2), 364-377. https://doi.org/10.1006/jmaa.2000.7354