### Abstract

Let E be a real uniformly smooth Banach space. Let A: D(A) = E → 2^{E} be an accretive operator that satisfies the range condition and A^{-1}(0) ≠. Let {λ_{n}} and {θ_{n}} be two real sequences satisfying appropriate conditions, and for z ∈ E arbitrary, let the sequence {x_{n}} be 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}, ≥ 0. Assume that {u_{n}} is bounded. It is proved that {x_{n}} converges strongly to Some x* ∈ A^{-1} (0). Furthermore, if K is a nonempty closed convex subset of E and T: K → K is a bounded continuous pseudocontractive map with F (T) := {Tx = x} ≠, it is proved that for arbitrary z ∈ K, the sequence {x_{n}} generated from x_{0} ∈ K by x_{n+1} = x_{n} - λ_{n} ((I - T)x_{n} + θ_{n} (x_{n} - z)), n ≥ 0,) where {λ_{n}} and {θ_{n}} are real sequences satisfying appropriate conditions, converges strongly to a fixed point of T.

Original language | English |
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Pages (from-to) | 756-765 |

Number of pages | 10 |

Journal | Journal of Mathematical Analysis and Applications |

Volume | 282 |

Issue number | 2 |

DOIs | |

Publication status | Published - Jun 15 2003 |

### All Science Journal Classification (ASJC) codes

- Analysis
- Applied Mathematics